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Identify and Perform Reflections

Students reflect figures across horizontal lines, vertical lines, and the lines y = x and y = −x on the coordinate plane. They find the image coordinates using reflection rules and verify that reflections preserve distances, angles, and map lines to lines.

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Identify and Perform Reflections

Grade 8 · Geometry: Transformations · question 1 of 3

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20 rungs. A star at the top.

C−8−6−4−22468−8−6−4−224680

After point C is reflected across the x-axis, what is the x-coordinate of C′?

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How it is taught

0:00 of 4:09

A reflection flips a figure across a mirror line.

Each point stays the same distance from that line, on the other side.

RSTU−8−6−4−22468−8−6−4−24680

Read it: Reflections across an axis

Segment KL flips across the x-axis. A flip keeps each point's distance from the mirror and moves it to the other side, so K(2, 5) lands at K′(2, −5).

  1. Find the mirror line.
  2. Across the x-axis, x stays and y changes sign: (x, y) → (x, −y).
  3. Across the y-axis, y stays and x changes sign: (x, y) → (−x, y).

K is 5 above the x-axis, so K′ is 5 below it.

The coordinate along the mirror does not change; the one across it changes sign.

Across the line y = x, the two coordinates swap places.

A reflection across an axis changes the sign of the coordinate across that axis.

Changing both signs, as if the flip were a half turn: K(2, 5) to (−2, −5).

Only the coordinate across the mirror changes. Across the x-axis that is y, so K′ is (2, −5).

Point Q(8, −4) is reflected across the x-axis. What is the y-coordinate of Q′? — 4. Across the x-axis, x stays and y changes sign: −4 becomes 4.

Reflect △ABC across the y-axis

A reflection flips a figure across a mirror line, just like looking into a mirror.

Here's our coordinate plane, with the x-axis and y-axis.

Triangle ABC sits in the right half of the plane.

Its vertices are A at one-one, B at four-one, and C at four-three.

Grade 8 · Flipping a triangle across a mirror line

Today our mirror is the y-axis — the vertical line where x equals zero.

Reflecting across the y-axis follows one rule: x, y becomes negative x, y. The y stays the same.

A is at one, one, so A-prime lands at negative one, one.

B is at four, one, so B-prime lands at negative four, one.

And C at four, three reflects to C-prime at negative four, three.

Now connect the new vertices to draw the reflected triangle.

Same shape, same size — each point sits the same distance from the y-axis.

Reflections preserve distances and angles. Triangle ABC has flipped across the y-axis to A-prime B-prime C-prime.

Now you try. Find the x-coordinate of A prime. What is x of A-prime?

What you see

While they climb, your page writes one true line to ask about tonight, and a short note each Sunday.

MayaGrade 3 · Mathematics
Did you know?

A chessboard has 64 squares — share them out between the 8 rows and each row holds exactly 8.

Today’s goal
1 star — one skill mastered, every rung of its ladder climbed
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Divide within 100

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MayaGrade 3 · Mathematics

Maya earned 2 stars this week — Interpret multiplication as equal groups, which took 6 answers over 3 days before its star landed 3 days ago and Multiply by 6, 7, 8 and 9. Next up: Divide within 100.

An example week.

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