Reflecting Shapes - Maths with Mum - Free Printable

Let’s solve each reflection problem step by step.

We are reflecting shapes over a line (either vertical or horizontal). To reflect a shape:
- For a vertical line (up-down dashed line): flip the shape left-to-right across that line. Each point moves the same distance to the other side.
- For a horizontal line (left-right dashed line): flip the shape up-and-down across that line. Each point moves the same distance above/below the line.

We’ll go one by one.

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a) Triangle reflected over a vertical red line.

Original triangle is on the right side of the line, 1 unit away from it.

After reflection: it will be on the left side, also 1 unit away — mirrored.

So if original points were at (say) x=4,5,6 and line is at x=3 → new points at x=2,1,0? Wait — let’s count grid squares carefully.

Actually, looking at the grid:

Assume the vertical red line is between columns. Let’s say column numbers start at 0 on left.

In part a), the triangle has vertices roughly at:
- Top: row 2, col 5
- Bottom-left: row 4, col 4
- Bottom-right: row 4, col 5

Red line is at col 3 (between col 3 and 4? Actually, looks like it's drawn *on* the line between col 3 and 4 — so we treat it as x = 3.5? But for simplicity in grid reflections, usually the line is on a grid line.

Wait — better approach: count how many units each point is from the mirror line, then place the reflected point the same distance on the other side.

In part a):

The triangle is entirely to the RIGHT of the red vertical line.

Distance from leftmost point of triangle to red line: 1 square.

So after reflection, the image should be 1 square to the LEFT of the red line.

Shape stays same size and orientation but flipped horizontally.

So reflected triangle will have:
- Top vertex: same row, but now 1 unit left of red line → if red line is at x=3, then top was at x=4 → now at x=2
- Similarly, bottom-left was at x=4 → now x=2; bottom-right was at x=5 → now x=1

Wait — actually, let me assign coordinates properly.

Set coordinate system: bottom-left corner of grid is (0,0), x increases right, y increases up.

But since it’s a grid, we can just use relative positions.

Easier: draw mentally.

Original triangle in a): pointing up, base on bottom, apex up. It’s sitting with its left edge touching the red line? No — there’s one empty column between red line and triangle.

Looking again: red line is vertical, triangle is to the right, separated by one full grid square.

So when reflected, it will appear on the left side, same distance — so one grid square to the left of red line.

And it will be mirrored — so instead of sloping down to the right, it will slope down to the left.

So final position: symmetric across the red line.

Same for others.

Let me do all quickly with care.

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a) Reflect triangle over vertical line.

Original: occupies columns 4–5 (if red line is at col 3), rows 2–4.

Reflected: should occupy columns 1–2 (since 3 - 1 = 2, 3 - 2 = 1), same rows.

Vertices:
Original: (4,4), (5,4), (4,2) [assuming bottom-left is (0,0)]

Mirror line x=3.

Reflection formula: x' = 2*mirror_x - x

So:
(4,4) → 2*3 - 4 = 2 → (2,4)
(5,4) → 6 - 5 = 1 → (1,4)
(4,2) → 6 - 4 = 2 → (2,2)

So reflected triangle has points at (1,4), (2,4), (2,2) — which is a triangle pointing left? Wait no — plotting: (1,4) and (2,4) form base, (2,2) is below — so it’s a right triangle with right angle at (2,4)? Actually, same shape, just flipped.

Yes.

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b) Diamond (square rotated) reflected over vertical red line.

Original diamond centered around col 5, red line at col 3? Distance: center at x=5, mirror at x=3 → distance 2 → reflected center at x=1.

Points of diamond: typically (5,3), (6,4), (5,5), (4,4) — assuming standard diamond.

Reflect over x=3:

(5,3) → 6-5=1 → (1,3)
(6,4) → 6-6=0 → (0,4)
(5,5) → 6-5=1 → (1,5)
(4,4) → 6-4=2 → (2,4)

So new diamond at (0,4), (1,5), (2,4), (1,3) — still a diamond, now on left side.

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c) Quadrilateral reflected over horizontal red line.

Horizontal line — so flip up/down.

Assume red line is at y=3 (middle of grid).

Original shape: below the line? Looking at image — in c), shape is below the horizontal red line.

Vertices approx: (2,1), (3,1), (3,2), (2,2) — wait, that’s a rectangle? But it’s tilted? Actually, looks like a parallelogram.

From image: points at (2,1), (3,2), (2,3)? Wait no — let's see.

Actually, in c), the blue shape is a quadrilateral with points roughly:
Bottom-left: (2,1)
Bottom-right: (3,1)
Top-right: (3,2)
Top-left: (2,2) — but that would be rectangle. But it’s drawn slanted? Maybe not.

Looking back — perhaps it’s a trapezoid or something.

To avoid confusion, let’s assume standard grid counting.

Suppose horizontal mirror line is at y=3.

Original shape is entirely below y=3, say from y=1 to y=2.

Then reflection will be above y=3, from y=4 to y=5.

Each point (x,y) reflects to (x, 2*3 - y) = (x, 6-y)

So if original points are:
A: (2,1) → (2,5)
B: (3,1) → (3,5)
C: (3,2) → (3,4)
D: (2,2) → (2,4)

So reflected shape is same shape, now above the line.

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d) Trapezoid reflected over horizontal red line.

Original above the line? In d), shape is above the horizontal red line.

Say red line at y=3.

Original points: e.g., (4,4), (6,4), (7,3), (5,3) — approximate.

Reflect over y=3: y' = 6 - y

So:
(4,4) → (4,2)
(6,4) → (6,2)
(7,3) → (7,3) — on the line, stays
(5,3) → (5,3)

So reflected shape below the line.

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e) Arrow pointing down, reflected over horizontal red line.

Arrow is above the line? In e), arrow is above the horizontal red line, pointing down toward it.

After reflection: it will be below the line, pointing up.

Because flipping over horizontal line reverses vertical direction.

Original arrow: say tip at (3,4), base from (2,6) to (4,6) — but simplified.

Actually, typical arrow: shaft from y=5 to y=3, head at y=3 pointing down.

Mirror at y=3? Or y=4? Looking at image — red line is below the arrow.

Assume red line at y=3.

Arrow extends from y=4 to y=6? Tip at y=4, base at y=6.

Reflect over y=3: y' = 6 - y

Tip: (3,4) → (3,2)
Base left: (2,6) → (2,0)
Base right: (4,6) → (4,0)

So reflected arrow points upward, with tip at (3,2), base at y=0.

But since grid may not go to y=0, perhaps adjust.

In any case, it flips vertically.

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f) L-shape reflected over vertical red line.

Original L is on left side of red line.

Red line vertical, say at x=5.

L-shape: e.g., points (3,2), (4,2), (5,2), (5,3), (5,4) — forming L.

Reflect over x=5: x' = 10 - x

So:
(3,2) → (7,2)
(4,2) → (6,2)
(5,2) → (5,2) — on line
(5,3) → (5,3)
(5,4) → (5,4)

So reflected L is on the right side, mirrored — so instead of extending right and up, it extends left and up? Wait no.

Original L: from (3,2) to (5,2) horizontal, then up to (5,4).

After reflection: from (7,2) to (5,2) horizontal (so leftward), then up to (5,4). So it’s an L facing left.

Yes.

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Now, to present the answer clearly for student:

Since this is a drawing task, I need to describe where each reflected shape goes.

But since user expects "final answer", and it's multiple parts, I'll list for each letter what the reflected shape looks like or its position.

However, the instruction says "solve the problem accurately" — and since it's a worksheet, probably they want the drawings, but I can't draw here.

Alternative: describe the coordinates or relative position.

But for educational assistant, best to explain how to do it, but options say ExplainAnswer is false.

Wait — user set ExplainAnswer: false, TeachTopic: false, GeneratePractice: false.

So only Final Answer is required.

But Final Answer must come after reasoning — and I did reasoning.

Now, for Final Answer, since it's multiple parts, I should provide the solution for each.

Perhaps: for each subpart, state the location or description of the reflected shape.

Since it's a grid, I can specify the new coordinates.

But to keep simple, I'll say:

For each shape, the reflection is created by flipping it over the red line, maintaining the same distance on the opposite side.

Specifically:

a) The triangle is flipped to the left of the vertical line, same height, mirrored horizontally.

b) The diamond is flipped to the left of the vertical line, centered symmetrically.

c) The quadrilateral is flipped to above the horizontal line, same width, mirrored vertically.

d) The trapezoid is flipped to below the horizontal line.

e) The arrow is flipped to below the horizontal line, now pointing upward.

f) The L-shape is flipped to the right of the vertical line, mirrored so it faces left.

But this is vague.

Better to give exact grid positions.

Assume each grid is 8x8 or something, but not specified.

From common worksheets, often grids are 10x10.

But to be precise, let's define for each.

Since the problem is to "reflect the following shapes", and no specific output format, I think for Final Answer, I can list the transformed coordinates or describe briefly.

But perhaps the expected answer is the drawn result, which I can't provide.

Another idea: since it's a homework helper, and user might need to draw it, I can instruct how to draw each.

But rules say: "provide only the final correct answer" after reasoning.

And "do not describe the image".

I think the best is to state for each part the key change.

Let me try to summarize concisely.

Final Answer:

a) Reflected triangle is on the left side of the vertical line, identical in size, mirrored horizontally.
b) Reflected diamond is on the left side of the vertical line, symmetric to original.
c) Reflected quadrilateral is above the horizontal line, mirrored vertically.
d) Reflected trapezoid is below the horizontal line.
e) Reflected arrow is below the horizontal line, pointing upward.
f) Reflected L-shape is on the right side of the vertical line, mirrored to face left.

But this is still descriptive.

Perhaps for math problems, they expect coordinates.

Let's assume the grid has lines at integer values, and red lines are at specific x or y.

From typical such worksheets:

In a), vertical red line is at x=3 (between columns 3 and 4? Or at column 3?).

To resolve, let's look at the first one.

In a), the triangle is in the fourth and fifth columns from left, red line is third column from left? Let's count.

Imagine the grid has columns 1 to 8 from left.

In a), red vertical line is after column 3, so at x=3.5? But usually in such problems, the line is on a grid line.

Upon second thought, in most school worksheets, the mirror line is drawn on a grid line, and shapes are on grid points.

For example, in a), the triangle has vertices at (4,2), (4,4), (5,4) if we set bottom-left as (1,1), but let's use (0,0) as bottom-left.

Set coordinate system: let the bottom-left corner of the entire grid be (0,0), x right, y up.

For part a):
- Red vertical line at x=3.
- Triangle vertices: (4,2), (4,4), (5,4) — wait, that would be a different shape.

Standard: if it's a right triangle with legs parallel to axes, but in image, it's not — it's oriented with hypotenuse.

From memory of such problems, in a), the triangle has points at (4,3), (4,5), (5,4) or something.

I think I'm overcomplicating.

For the purpose of this response, since the user needs to complete the worksheet, and I can't draw, the Final Answer should be a description that allows them to draw it correctly.

So I'll go with:

For each shape, to reflect it:
- Measure the perpendicular distance from each vertex to the mirror line.
- On the other side of the line, mark a point at the same distance.
- Connect those points to form the reflected shape.

Specifically for each:

a) The triangle is reflected to the left of the vertical line. If the original is 1 unit right of the line, the reflection is 1 unit left. The shape is flipped horizontally.

b) The diamond is reflected to the left of the vertical line, maintaining its size and orientation relative to the line.

c) The quadrilateral is reflected above the horizontal line. If it was 1 unit below, it's now 1 unit above, flipped vertically.

d) The trapezoid is reflected below the horizontal line.

e) The arrow is reflected below the horizontal line, and since it was pointing down, it now points up.

f) The L-shape is reflected to the right of the vertical line, and its orientation is mirrored (the short arm now points left instead of right).

This should suffice for the student to complete the drawing.

So Final Answer:

a) Draw the triangle mirrored on the left side of the vertical red line, same distance.
b) Draw the diamond mirrored on the left side of the vertical red line.
c) Draw the quadrilateral mirrored above the horizontal red line.
d) Draw the trapezoid mirrored below the horizontal red line.
e) Draw the arrow mirrored below the horizontal red line, pointing upward.
f) Draw the L-shape mirrored on the right side of the vertical red line, with the bend facing left.

Yes.