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Reflections on the Coordinate Plane — Easy Worksheet 1
Grade 8 · Whoobee Name: ____________________ Date: __________
Draw the image of each figure after the reflection, then answer the question. Write points as (x, y).
How to solve
A reflection flips a figure over a line, so each image point is the same distance from the line as the original, on the other side. Across the x-axis: (x, y) → (x, −y). Across the y-axis: (x, y) → (−x, y). Across y = x: swap the coordinates, (x, y) → (y, x). Across y = −x: swap and change both signs, (x, y) → (−y, −x). Across a line like x = 2, count how far each point is from the line and go the same distance past it.
Example
Reflect quadrilateral EFGH across the x-axis. What are the coordinates of E′?
Not quite. The answer is
💡 Across the y-axis, (x, y) → (−x, y): change the sign of x and keep y. D(−5, 0) → D′(5, 0). So D′ is (5, 0).
✓ Correct!
Not quite. The answer is
💡 Across the y-axis, (x, y) → (−x, y): change the sign of x and keep y. D(−5, 0) → D′(5, 0). So D′ is (5, 0).
💡 How to solve: Reflections on the Coordinate Plane
A reflection flips a figure over a line, so each image point is the same distance from the line as the original, on the other side. Across the x-axis: (x, y) → (x, −y). Across the y-axis: (x, y) → (−x, y). Across y = x: swap the coordinates, (x, y) → (y, x). Across y = −x: swap and change both signs, (x, y) → (−y, −x). Across a line like x = 2, count how far each point is from the line and go the same distance past it.
Try a similar one
Reflect triangle JKL across the y-axis. What are the coordinates of L′?
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 Compare a vertex with its image: P(−2, 4) → P′(−2, −4). x stayed the same and y changed sign. That is (x, y) → (x, −y), a reflection across the x-axis.
✓ Correct!
Not quite. The answer is
💡 Compare a vertex with its image: P(−2, 4) → P′(−2, −4). x stayed the same and y changed sign. That is (x, y) → (x, −y), a reflection across the x-axis.
💡 How to solve: Reflections on the Coordinate Plane
A reflection flips a figure over a line, so each image point is the same distance from the line as the original, on the other side. Across the x-axis: (x, y) → (x, −y). Across the y-axis: (x, y) → (−x, y). Across y = x: swap the coordinates, (x, y) → (y, x). Across y = −x: swap and change both signs, (x, y) → (−y, −x). Across a line like x = 2, count how far each point is from the line and go the same distance past it.
Try a similar one
Reflect triangle XYZ across the y-axis. What are the coordinates of Y′?
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 Across the y-axis, (x, y) → (−x, y): change the sign of x and keep y. R(7, 1) → R′(−7, 1). So R′ is (−7, 1).
✓ Correct!
Not quite. The answer is
💡 Across the y-axis, (x, y) → (−x, y): change the sign of x and keep y. R(7, 1) → R′(−7, 1). So R′ is (−7, 1).
💡 How to solve: Reflections on the Coordinate Plane
A reflection flips a figure over a line, so each image point is the same distance from the line as the original, on the other side. Across the x-axis: (x, y) → (x, −y). Across the y-axis: (x, y) → (−x, y). Across y = x: swap the coordinates, (x, y) → (y, x). Across y = −x: swap and change both signs, (x, y) → (−y, −x). Across a line like x = 2, count how far each point is from the line and go the same distance past it.
Try a similar one
Reflect quadrilateral PQRS across the x-axis. What are the coordinates of S′?
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 Across the x-axis, (x, y) → (x, −y): keep x and change the sign of y. P(2, −1) → P′(2, 1). So P′ is (2, 1).
✓ Correct!
Not quite. The answer is
💡 Across the x-axis, (x, y) → (x, −y): keep x and change the sign of y. P(2, −1) → P′(2, 1). So P′ is (2, 1).
💡 How to solve: Reflections on the Coordinate Plane
A reflection flips a figure over a line, so each image point is the same distance from the line as the original, on the other side. Across the x-axis: (x, y) → (x, −y). Across the y-axis: (x, y) → (−x, y). Across y = x: swap the coordinates, (x, y) → (y, x). Across y = −x: swap and change both signs, (x, y) → (−y, −x). Across a line like x = 2, count how far each point is from the line and go the same distance past it.
Try a similar one
Reflect quadrilateral ABCD across the x-axis. What are the coordinates of A′?
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 Across the x-axis, (x, y) → (x, −y): keep x and change the sign of y. B(3, −7) → B′(3, 7). So B′ is (3, 7).
✓ Correct!
Not quite. The answer is
💡 Across the x-axis, (x, y) → (x, −y): keep x and change the sign of y. B(3, −7) → B′(3, 7). So B′ is (3, 7).
💡 How to solve: Reflections on the Coordinate Plane
A reflection flips a figure over a line, so each image point is the same distance from the line as the original, on the other side. Across the x-axis: (x, y) → (x, −y). Across the y-axis: (x, y) → (−x, y). Across y = x: swap the coordinates, (x, y) → (y, x). Across y = −x: swap and change both signs, (x, y) → (−y, −x). Across a line like x = 2, count how far each point is from the line and go the same distance past it.
Try a similar one
Reflect triangle JKL across the x-axis. What are the coordinates of J′?
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 Compare a vertex with its image: E(−6, −1) → E′(6, −1). x changed sign and y stayed the same. That is (x, y) → (−x, y), a reflection across the y-axis.
✓ Correct!
Not quite. The answer is
💡 Compare a vertex with its image: E(−6, −1) → E′(6, −1). x changed sign and y stayed the same. That is (x, y) → (−x, y), a reflection across the y-axis.
💡 How to solve: Reflections on the Coordinate Plane
A reflection flips a figure over a line, so each image point is the same distance from the line as the original, on the other side. Across the x-axis: (x, y) → (x, −y). Across the y-axis: (x, y) → (−x, y). Across y = x: swap the coordinates, (x, y) → (y, x). Across y = −x: swap and change both signs, (x, y) → (−y, −x). Across a line like x = 2, count how far each point is from the line and go the same distance past it.
Try a similar one
Reflect quadrilateral EFGH across the x-axis. What are the coordinates of H′?
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 Across the x-axis, (x, y) → (x, −y): keep x and change the sign of y. J(4, −6) → J′(4, 6). So J′ is (4, 6).
✓ Correct!
Not quite. The answer is
💡 Across the x-axis, (x, y) → (x, −y): keep x and change the sign of y. J(4, −6) → J′(4, 6). So J′ is (4, 6).
💡 How to solve: Reflections on the Coordinate Plane
A reflection flips a figure over a line, so each image point is the same distance from the line as the original, on the other side. Across the x-axis: (x, y) → (x, −y). Across the y-axis: (x, y) → (−x, y). Across y = x: swap the coordinates, (x, y) → (y, x). Across y = −x: swap and change both signs, (x, y) → (−y, −x). Across a line like x = 2, count how far each point is from the line and go the same distance past it.
Try a similar one
Reflect quadrilateral ABCD across the x-axis. What are the coordinates of D′?
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 Across the x-axis, (x, y) → (x, −y): keep x and change the sign of y. P(−6, 6) → P′(−6, −6). So P′ is (−6, −6).
✓ Correct!
Not quite. The answer is
💡 Across the x-axis, (x, y) → (x, −y): keep x and change the sign of y. P(−6, 6) → P′(−6, −6). So P′ is (−6, −6).
💡 How to solve: Reflections on the Coordinate Plane
A reflection flips a figure over a line, so each image point is the same distance from the line as the original, on the other side. Across the x-axis: (x, y) → (x, −y). Across the y-axis: (x, y) → (−x, y). Across y = x: swap the coordinates, (x, y) → (y, x). Across y = −x: swap and change both signs, (x, y) → (−y, −x). Across a line like x = 2, count how far each point is from the line and go the same distance past it.
Try a similar one
Reflect triangle XYZ across the x-axis. What are the coordinates of Z′?
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
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Reflections on the Coordinate Plane — Easy Worksheet 1
Draw the image of each figure after the reflection, then answer the question. Write points as (x, y).