Let’s work through each reflection problem step by step.
We are given 6 figures on coordinate grids, and for each, we need to reflect the figure across a specified line. Since this is a visual task and we can’t draw here, I’ll describe exactly how to perform each reflection — including which points move where — so you can do it yourself on paper or in your mind.
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Problem 1: Reflection Across Line y = -x
Original shape: A small “L” shape in the third quadrant (left and down from origin).
Rule for reflecting over y = -x:
→ Swap x and y, then change both signs.
So point (a, b) becomes (-b, -a)
Example: If a corner is at (-3, -1), its reflection is (1, 3)
Do this for all corners of the L-shape. The reflected shape will be in the first quadrant, rotated and flipped.
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Problem 2: Reflection Across Line y = x
Original shape: A triangle in the second quadrant (left and up).
Rule for reflecting over y = x:
→ Swap x and y.
So point (a, b) becomes (b, a)
Example: Point (-4, 2) becomes (2, -4)
Reflect all three vertices. The new triangle will be in the fourth quadrant.
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Problem 3: Reflection Across the line x = 1
Original shape: A rectangle in the first quadrant, starting near x=2.
Rule: For vertical line x = h, reflection of point (a, b) is (2h - a, b)
Here, h = 1 → new x = 2(1) - a = 2 - a
Example: Point (2, 4) → (2 - 2, 4) = (0, 4)
Point (4, 4) → (2 - 4, 4) = (-2, 4)
The rectangle flips left across x=1. It will now span from x=-2 to x=0.
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Problem 4: Reflection Across the y-axis
Original shape: A triangle in the first quadrant.
Rule: Reflecting over y-axis → change sign of x-coordinate.
Point (a, b) → (-a, b)
Example: (5, 0) → (-5, 0); (1, 4) → (-1, 4)
Triangle moves to the second quadrant, mirrored horizontally.
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Problem 5: Reflection Across the line y = 2
Original shape: A parallelogram above y=2.
Rule: For horizontal line y = k, reflection of (a, b) is (a, 2k - b)
Here, k = 2 → new y = 4 - b
Example: Point (2, 4) → (2, 4 - 4) = (2, 0)
Point (3, 5) → (3, 4 - 5) = (3, -1)
Shape flips downward across y=2. Some parts may go below the x-axis.
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Problem 6: Reflection Across the x-axis
Original shape: An L-shape in the fourth quadrant (right and down).
Rule: Reflecting over x-axis → change sign of y-coordinate.
Point (a, b) → (a, -b)
Example: (3, -2) → (3, 2); (4, -4) → (4, 4)
L-shape flips upward into the first quadrant.
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✔ All reflections follow standard rules. You can verify by checking that each point is the same distance from the mirror line but on the opposite side.
Final Answer:
To complete the worksheet, reflect each figure using these rules:
1) Swap x and y, then negate both → (a,b) → (-b,-a)
2) Swap x and y → (a,b) → (b,a)
3) Flip over x=1 → (a,b) → (2−a, b)
4) Flip over y-axis → (a,b) → (−a, b)
5) Flip over y=2 → (a,b) → (a, 4−b)
6) Flip over x-axis → (a,b) → (a, −b)
Draw the reflected shapes accordingly on each grid.
Parent Tip: Review the logic above to help your child master the concept of translation rotation reflection worksheet answers.
