Grade 5 Math worksheet focusing on reflection, where students draw the mirror image of various shapes across a vertical line on a grid.
Grade 5 Math worksheet on reflection of shapes on a grid, featuring six exercises to draw accurate reflections across a vertical line of symmetry.
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Show Answer Key & Explanations
Step-by-step solution for: Worksheet Grade 5 Math Reflection | Reflection math, Math ...
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Show Answer Key & Explanations
Step-by-step solution for: Worksheet Grade 5 Math Reflection | Reflection math, Math ...
To solve these reflection problems, we need to flip each shape across the red lines (the axes of reflection). Think of the red lines as mirrors. The reflected shape must be the same distance from the mirror line as the original shape, but on the opposite side.
Here is the step-by-step solution for each problem:
1. Square Reflection
* Original Shape: A 3x3 square located in the top-left quadrant. Its right edge is 1 unit away from the vertical red line. Its bottom edge is 2 units above the horizontal red line.
* Reflection Rule: Since the shape is only on one side of the vertical axis, we reflect it horizontally across the vertical red line.
* New Position: The reflected square will be in the top-right quadrant. Its left edge will be 1 unit away from the vertical red line. It stays at the same height (bottom edge 2 units above the horizontal line).
* Result: Draw a 3x3 square in the top-right quadrant, starting 1 grid unit to the right of the center vertical line and 2 grid units up from the center horizontal line.
2. Cross Shape Reflection
* Original Shape: A "plus" sign made of 5 squares. It is entirely in the top-right quadrant. The leftmost part of the cross is 1 unit away from the vertical red line. The bottom part of the cross is 1 unit above the horizontal red line.
* Reflection Rule: Reflect horizontally across the vertical red line.
* New Position: The reflected cross will be in the top-left quadrant. Its rightmost part will be 1 unit away from the vertical red line. The height remains the same.
* Result: Draw the same "plus" sign in the top-left quadrant. The central square of the cross should be 2 units left of the vertical line and 2 units above the horizontal line.
3. Triangle Reflection
* Original Shape: An isosceles triangle in the top-left quadrant. The base is 4 units wide and sits 2 units above the horizontal red line. The tip is on the vertical red line? No, looking closely, the triangle's base spans from x=-3 to x=-1 (relative to center) or similar. Let's count grids.
* Center intersection is (0,0).
* Triangle vertices: Bottom-left (-3, 2), Bottom-right (-1, 2), Top (-2, 4). Wait, let's look closer.
* Actually, the triangle base is 4 units wide. It looks like it goes from 3 units left of the vertical line to 1 unit left of the vertical line. So x = -3 to x = -1. The height is 2 units (from y=2 to y=4). The peak is at x=-2.
* Reflection Rule: Reflect horizontally across the vertical red line.
* New Position: The x-coordinates flip signs.
* New Bottom-left: (1, 2) -> 1 unit right of vertical line, 2 units up.
* New Bottom-right: (3, 2) -> 3 units right of vertical line, 2 units up.
* New Peak: (2, 4) -> 2 units right of vertical line, 4 units up.
* Result: Draw an identical triangle in the top-right quadrant. Its base is 2 units above the horizontal line, spanning from 1 unit to 3 units to the right of the vertical line. The peak is 4 units up and 2 units to the right of the vertical line.
4. L-Shape Reflection
* Original Shape: An L-shape in the top-right quadrant.
* Vertical part: 2 units wide, 3 units high. Located 1 unit right of vertical axis, extending from y=4 to y=7? Let's trace carefully.
* It looks like a block of 2x2 on top, and a 1x1 hanging off the bottom right? Or standard L?
* Let's trace coordinates relative to center (0,0):
* Top-left corner of shape: (1, 5). Width 2, Height 2 for the top block? No.
* Let's assume standard grid counting. The shape is composed of squares.
* Top row: 2 squares wide. Starts 1 unit right of axis. So x=1 to 3. Y level: let's say 6 to 8.
* Bottom part: Extends down from the right side.
* Actually, simpler approach: Mirror every point horizontally.
* The shape is in the top-right. The reflection will be in the top-left.
* Distance from vertical axis: The leftmost edge of the original is 1 unit from the axis. The reflected shape's rightmost edge will be 1 unit from the axis (on the left side).
* The shape extends 3 units to the right (width 3?). Let's look at shape 4 again. It looks like a 2-wide column on the left, and a 1-wide extension to the right at the bottom? Or vice versa.
* Let's look at the "notch". It's an inverted L or a step.
* Original: Top part is 2 units wide. Bottom part sticks out to the right by 1 more unit? No, it looks like a 2x2 square with a 1x1 attached to the bottom right.
* Total width: 3 units. Total height: 3 units.
* Left edge is at x=1. Right edge is at x=4. Bottom edge is at y=3. Top edge is at y=6.
* Reflection: Flip x-coordinates.
* New Right edge (was left): x=-1.
* New Left edge (was right): x=-4.
* Y-coordinates stay same: y=3 to y=6.
* Shape orientation flips horizontally. The part that stuck out to the right will now stick out to the left.
* Result: Draw the mirrored L-shape in the top-left quadrant. The main vertical block is adjacent to the axis (starting 1 unit left), and the "foot" sticks out further to the left.
5. Diamond (Rhombus) Reflection
* Original Shape: A diamond in the bottom-left quadrant.
* Top vertex: On the horizontal axis? No, it looks like it touches the horizontal axis at x=-2? Let's check.
* The diamond is centered at roughly (-2, -2).
* Vertices: Top (-2, 0), Bottom (-2, -4), Left (-4, -2), Right (0, -2)?
* Looking closely at image 5: The right vertex of the diamond seems to touch the vertical red line. The top vertex seems to touch the horizontal red line.
* If Right Vertex is at (0, -2) and Top Vertex is at (-2, 0):
* Center is (-2, -2).
* Left Vertex: (-4, -2).
* Bottom Vertex: (-2, -4).
* Reflection Rule: This is tricky. Usually, reflections are across one axis. The prompt says "Draw the accurately reflection". There are two red lines. However, in previous questions, the shapes were clearly reflecting across just the vertical or just the horizontal based on position. But here, the shape is in one quadrant.
* Standard convention for these worksheets: If a vertical line is drawn through the middle, you reflect across the vertical line. If a horizontal line is drawn, you reflect across the horizontal. Here BOTH are drawn.
* Let's look at Q1, Q2, Q3, Q4, Q6. In all those, the shape is in one quadrant, and the reflection is typically across the nearest axis or the vertical axis is the primary "mirror" for left/right swaps.
* However, often "Reflection" with two axes implies reflecting across the vertical axis unless specified otherwise. Let's assume reflection across the vertical red line, as that is the standard "y-axis" reflection taught first.
* Reflecting the diamond across the vertical red line (y-axis):
* Original Right Vertex (0, -2) stays at (0, -2) because it's on the axis.
* Original Top Vertex (-2, 0) becomes (2, 0).
* Original Left Vertex (-4, -2) becomes (4, -2).
* Original Bottom Vertex (-2, -4) becomes (2, -4).
* So the new diamond is in the bottom-right quadrant. It touches the vertical axis at the top-middle of its left side? No, the vertex is on the axis.
* Result: A diamond in the bottom-right quadrant. Its leftmost point touches the vertical red line at 2 units down. Its topmost point touches the horizontal red line at 2 units right.
6. L-Shape Reflection
* Original Shape: An L-shape in the bottom-right quadrant.
* It looks like a vertical column of 3 squares, with a horizontal base of 2 squares extending to the left?
* Let's trace: Bottom-right corner is at (4, -4)?
* Let's assume the inner corner is near the axis.
* The shape is 2 units wide and 3 units high.
* Left edge is at x=1. Right edge is at x=3.
* Top edge is at y=-1. Bottom edge is at y=-4? Or y=-3?
* Let's count: From horizontal line down: 1 empty, then shape starts? No, shape seems to start 1 unit down.
* Let's assume:
* Vertical bar: x=2 to 3, y=-1 to -3.
* Horizontal bar: x=1 to 2, y=-3 to -4?
* Actually, it looks like a standard "L". Vertical part on the right, horizontal part on the bottom extending left.
* Coordinates:
* Right edge: x=3. Left edge: x=1.
* Top edge: y=-1. Bottom edge: y=-4.
* Wait, let's look at the "step".
* It looks like a 2x2 square at the bottom (x=1 to 3, y=-3 to -1? No).
* Let's try: A 1-unit wide column on the right (x=2 to 3) going from y=-1 to -4 (height 3). And a 1-unit high row at the bottom (y=-3 to -4?) extending left to x=1.
* Let's just mirror the visual pattern.
* Original is in Bottom-Right.
* Reflection across Vertical Axis -> Moves to Bottom-Left.
* The shape is flipped horizontally.
* The vertical part was on the right side of the shape; now it will be on the left side of the reflected shape.
* The horizontal foot pointed left; now it will point right.
* Distance from axis: The closest part is 1 unit from the vertical axis. The reflected shape will also start 1 unit from the vertical axis (on the left side).
* Result: Draw the mirrored L-shape in the bottom-left quadrant. The vertical spine is on the left (closest to the axis), and the foot extends to the right (away from the axis).
Summary of Final Answers to Draw:
1. Top-Right Quadrant: A 3x3 square. Its left side is 1 grid unit from the vertical red line. Its bottom side is 2 grid units above the horizontal red line.
2. Top-Left Quadrant: A "plus" sign (cross). Its rightmost edge is 1 grid unit from the vertical red line. Its bottom edge is 1 grid unit above the horizontal red line.
3. Top-Right Quadrant: A triangle. Base is 2 grid units above the horizontal line. The base spans from 1 unit right to 3 units right of the vertical line. The peak is 4 units up and 2 units right of the vertical line.
4. Top-Left Quadrant: The mirrored L/step shape. The main block is adjacent to the vertical axis (starting 1 unit left). The protruding part points to the left.
5. Bottom-Right Quadrant: A diamond. Its left vertex touches the vertical red line at 2 units below the horizontal line. Its top vertex touches the horizontal red line at 2 units to the right of the vertical line.
6. Bottom-Left Quadrant: The mirrored L-shape. The vertical part is on the left (closest to the axis, starting 1 unit left). The bottom foot extends to the right (towards the axis).
Final Answer:
See the descriptions above for exactly where to draw each shape.
1. Draw a 3x3 square in the top-right box, shifted 1 unit right and 2 units up from the center.
2. Draw a cross in the top-left box, shifted 1 unit left and 1 unit up from the center.
3. Draw a triangle in the top-right box, with its base 2 units up and spanning 1–3 units right from the center.
4. Draw the reflected step-shape in the top-left box, mirroring the original horizontally.
5. Draw a diamond in the bottom-right box, touching the center lines at (2,0) and (0,-2).
6. Draw the reflected L-shape in the bottom-left box, mirroring the original horizontally.
Here is the step-by-step solution for each problem:
1. Square Reflection
* Original Shape: A 3x3 square located in the top-left quadrant. Its right edge is 1 unit away from the vertical red line. Its bottom edge is 2 units above the horizontal red line.
* Reflection Rule: Since the shape is only on one side of the vertical axis, we reflect it horizontally across the vertical red line.
* New Position: The reflected square will be in the top-right quadrant. Its left edge will be 1 unit away from the vertical red line. It stays at the same height (bottom edge 2 units above the horizontal line).
* Result: Draw a 3x3 square in the top-right quadrant, starting 1 grid unit to the right of the center vertical line and 2 grid units up from the center horizontal line.
2. Cross Shape Reflection
* Original Shape: A "plus" sign made of 5 squares. It is entirely in the top-right quadrant. The leftmost part of the cross is 1 unit away from the vertical red line. The bottom part of the cross is 1 unit above the horizontal red line.
* Reflection Rule: Reflect horizontally across the vertical red line.
* New Position: The reflected cross will be in the top-left quadrant. Its rightmost part will be 1 unit away from the vertical red line. The height remains the same.
* Result: Draw the same "plus" sign in the top-left quadrant. The central square of the cross should be 2 units left of the vertical line and 2 units above the horizontal line.
3. Triangle Reflection
* Original Shape: An isosceles triangle in the top-left quadrant. The base is 4 units wide and sits 2 units above the horizontal red line. The tip is on the vertical red line? No, looking closely, the triangle's base spans from x=-3 to x=-1 (relative to center) or similar. Let's count grids.
* Center intersection is (0,0).
* Triangle vertices: Bottom-left (-3, 2), Bottom-right (-1, 2), Top (-2, 4). Wait, let's look closer.
* Actually, the triangle base is 4 units wide. It looks like it goes from 3 units left of the vertical line to 1 unit left of the vertical line. So x = -3 to x = -1. The height is 2 units (from y=2 to y=4). The peak is at x=-2.
* Reflection Rule: Reflect horizontally across the vertical red line.
* New Position: The x-coordinates flip signs.
* New Bottom-left: (1, 2) -> 1 unit right of vertical line, 2 units up.
* New Bottom-right: (3, 2) -> 3 units right of vertical line, 2 units up.
* New Peak: (2, 4) -> 2 units right of vertical line, 4 units up.
* Result: Draw an identical triangle in the top-right quadrant. Its base is 2 units above the horizontal line, spanning from 1 unit to 3 units to the right of the vertical line. The peak is 4 units up and 2 units to the right of the vertical line.
4. L-Shape Reflection
* Original Shape: An L-shape in the top-right quadrant.
* Vertical part: 2 units wide, 3 units high. Located 1 unit right of vertical axis, extending from y=4 to y=7? Let's trace carefully.
* It looks like a block of 2x2 on top, and a 1x1 hanging off the bottom right? Or standard L?
* Let's trace coordinates relative to center (0,0):
* Top-left corner of shape: (1, 5). Width 2, Height 2 for the top block? No.
* Let's assume standard grid counting. The shape is composed of squares.
* Top row: 2 squares wide. Starts 1 unit right of axis. So x=1 to 3. Y level: let's say 6 to 8.
* Bottom part: Extends down from the right side.
* Actually, simpler approach: Mirror every point horizontally.
* The shape is in the top-right. The reflection will be in the top-left.
* Distance from vertical axis: The leftmost edge of the original is 1 unit from the axis. The reflected shape's rightmost edge will be 1 unit from the axis (on the left side).
* The shape extends 3 units to the right (width 3?). Let's look at shape 4 again. It looks like a 2-wide column on the left, and a 1-wide extension to the right at the bottom? Or vice versa.
* Let's look at the "notch". It's an inverted L or a step.
* Original: Top part is 2 units wide. Bottom part sticks out to the right by 1 more unit? No, it looks like a 2x2 square with a 1x1 attached to the bottom right.
* Total width: 3 units. Total height: 3 units.
* Left edge is at x=1. Right edge is at x=4. Bottom edge is at y=3. Top edge is at y=6.
* Reflection: Flip x-coordinates.
* New Right edge (was left): x=-1.
* New Left edge (was right): x=-4.
* Y-coordinates stay same: y=3 to y=6.
* Shape orientation flips horizontally. The part that stuck out to the right will now stick out to the left.
* Result: Draw the mirrored L-shape in the top-left quadrant. The main vertical block is adjacent to the axis (starting 1 unit left), and the "foot" sticks out further to the left.
5. Diamond (Rhombus) Reflection
* Original Shape: A diamond in the bottom-left quadrant.
* Top vertex: On the horizontal axis? No, it looks like it touches the horizontal axis at x=-2? Let's check.
* The diamond is centered at roughly (-2, -2).
* Vertices: Top (-2, 0), Bottom (-2, -4), Left (-4, -2), Right (0, -2)?
* Looking closely at image 5: The right vertex of the diamond seems to touch the vertical red line. The top vertex seems to touch the horizontal red line.
* If Right Vertex is at (0, -2) and Top Vertex is at (-2, 0):
* Center is (-2, -2).
* Left Vertex: (-4, -2).
* Bottom Vertex: (-2, -4).
* Reflection Rule: This is tricky. Usually, reflections are across one axis. The prompt says "Draw the accurately reflection". There are two red lines. However, in previous questions, the shapes were clearly reflecting across just the vertical or just the horizontal based on position. But here, the shape is in one quadrant.
* Standard convention for these worksheets: If a vertical line is drawn through the middle, you reflect across the vertical line. If a horizontal line is drawn, you reflect across the horizontal. Here BOTH are drawn.
* Let's look at Q1, Q2, Q3, Q4, Q6. In all those, the shape is in one quadrant, and the reflection is typically across the nearest axis or the vertical axis is the primary "mirror" for left/right swaps.
* However, often "Reflection" with two axes implies reflecting across the vertical axis unless specified otherwise. Let's assume reflection across the vertical red line, as that is the standard "y-axis" reflection taught first.
* Reflecting the diamond across the vertical red line (y-axis):
* Original Right Vertex (0, -2) stays at (0, -2) because it's on the axis.
* Original Top Vertex (-2, 0) becomes (2, 0).
* Original Left Vertex (-4, -2) becomes (4, -2).
* Original Bottom Vertex (-2, -4) becomes (2, -4).
* So the new diamond is in the bottom-right quadrant. It touches the vertical axis at the top-middle of its left side? No, the vertex is on the axis.
* Result: A diamond in the bottom-right quadrant. Its leftmost point touches the vertical red line at 2 units down. Its topmost point touches the horizontal red line at 2 units right.
6. L-Shape Reflection
* Original Shape: An L-shape in the bottom-right quadrant.
* It looks like a vertical column of 3 squares, with a horizontal base of 2 squares extending to the left?
* Let's trace: Bottom-right corner is at (4, -4)?
* Let's assume the inner corner is near the axis.
* The shape is 2 units wide and 3 units high.
* Left edge is at x=1. Right edge is at x=3.
* Top edge is at y=-1. Bottom edge is at y=-4? Or y=-3?
* Let's count: From horizontal line down: 1 empty, then shape starts? No, shape seems to start 1 unit down.
* Let's assume:
* Vertical bar: x=2 to 3, y=-1 to -3.
* Horizontal bar: x=1 to 2, y=-3 to -4?
* Actually, it looks like a standard "L". Vertical part on the right, horizontal part on the bottom extending left.
* Coordinates:
* Right edge: x=3. Left edge: x=1.
* Top edge: y=-1. Bottom edge: y=-4.
* Wait, let's look at the "step".
* It looks like a 2x2 square at the bottom (x=1 to 3, y=-3 to -1? No).
* Let's try: A 1-unit wide column on the right (x=2 to 3) going from y=-1 to -4 (height 3). And a 1-unit high row at the bottom (y=-3 to -4?) extending left to x=1.
* Let's just mirror the visual pattern.
* Original is in Bottom-Right.
* Reflection across Vertical Axis -> Moves to Bottom-Left.
* The shape is flipped horizontally.
* The vertical part was on the right side of the shape; now it will be on the left side of the reflected shape.
* The horizontal foot pointed left; now it will point right.
* Distance from axis: The closest part is 1 unit from the vertical axis. The reflected shape will also start 1 unit from the vertical axis (on the left side).
* Result: Draw the mirrored L-shape in the bottom-left quadrant. The vertical spine is on the left (closest to the axis), and the foot extends to the right (away from the axis).
Summary of Final Answers to Draw:
1. Top-Right Quadrant: A 3x3 square. Its left side is 1 grid unit from the vertical red line. Its bottom side is 2 grid units above the horizontal red line.
2. Top-Left Quadrant: A "plus" sign (cross). Its rightmost edge is 1 grid unit from the vertical red line. Its bottom edge is 1 grid unit above the horizontal red line.
3. Top-Right Quadrant: A triangle. Base is 2 grid units above the horizontal line. The base spans from 1 unit right to 3 units right of the vertical line. The peak is 4 units up and 2 units right of the vertical line.
4. Top-Left Quadrant: The mirrored L/step shape. The main block is adjacent to the vertical axis (starting 1 unit left). The protruding part points to the left.
5. Bottom-Right Quadrant: A diamond. Its left vertex touches the vertical red line at 2 units below the horizontal line. Its top vertex touches the horizontal red line at 2 units to the right of the vertical line.
6. Bottom-Left Quadrant: The mirrored L-shape. The vertical part is on the left (closest to the axis, starting 1 unit left). The bottom foot extends to the right (towards the axis).
Final Answer:
See the descriptions above for exactly where to draw each shape.
1. Draw a 3x3 square in the top-right box, shifted 1 unit right and 2 units up from the center.
2. Draw a cross in the top-left box, shifted 1 unit left and 1 unit up from the center.
3. Draw a triangle in the top-right box, with its base 2 units up and spanning 1–3 units right from the center.
4. Draw the reflected step-shape in the top-left box, mirroring the original horizontally.
5. Draw a diamond in the bottom-right box, touching the center lines at (2,0) and (0,-2).
6. Draw the reflected L-shape in the bottom-left box, mirroring the original horizontally.
Parent Tip: Review the logic above to help your child master the concept of reflections math worksheet.
