Geometry
Reflection
A reflection flips a figure over a line of reflection. Over the x-axis: (x, y) → (x, −y). Over the y-axis: (x, y) → (−x, y). Over y = x: (x, y) → (y, x).
Visualize It
Reflection flips a figure over a line
Watch & Learn
Watch a clear, friendly video explanation of Reflection:
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Worked Examples
Follow along with these step-by-step examples. Take your time — there's no rush!
Problem
Reflect (4, −3) over the x-axis
Reflect over x-axis
Step-by-Step Solution
Over x-axis: (x, y) → (x, −y)
(4, −3) → (4, 3)
Answer
(4, 3)
Problem
Reflect (−2, 5) over the y-axis
Reflect over y-axis
Step-by-Step Solution
Over y-axis: (x, y) → (−x, y)
(−2, 5) → (2, 5)
Answer
(2, 5)
Problem
Reflect (3, 7) over the line y = x
Reflect over y = x
Step-by-Step Solution
Over y = x: (x, y) → (y, x)
(3, 7) → (7, 3)
Answer
(7, 3)
Problem
Reflect the point (−5, −2) over the x-axis
Reflect (−5,−2) over x-axis
Step-by-Step Solution
Over x-axis: (x, y) → (x, −y)
(−5, −2) → (−5, 2)
Answer
(−5, 2)
Problem
A triangle has vertices (1, 2), (3, 4), (5, 1). Reflect over the y-axis.
Triangle reflected over y-axis
Step-by-Step Solution
Over y-axis: (x, y) → (−x, y)
(1, 2) → (−1, 2)
(3, 4) → (−3, 4)
(5, 1) → (−5, 1)
Answer
(−1, 2), (−3, 4), (−5, 1)
Your Turn — Practice Problems
Try all 5 problems on your own first. Write out your work — that's how it sticks!
💡 Tip: Don't peek at the answers until you've genuinely tried each one.
Reflect (5, 2) over the x-axis
Reflect (−4, 6) over the y-axis
Reflect (1, 8) over y = x
Reflect (−3, −5) over the x-axis
Reflect (7, 0) over the y-axis
Reflect (0, 4) over the x-axis
Reflect (−2, 3) over y = x
Reflect (6, −1) over the y-axis
Reflect (−5, 0) over the x-axis
Reflect (4, 9) over y = x
Reflect (−3, −7) over the y-axis
Reflect (2, 2) over y = x
Finished all 12? Give yourself a pat on the back — then check your work!
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