Graphs · On the grid · 2.3

Reflect a point.

Reflecting a point across the x-axis flips the sign of y; across the y-axis flips the sign of x. (3, 2) reflected over the x-axis is (3, −2).

01 / THE IDEA

See it work.

Watch the method

Reflect a point

(3, 2) over the x-axis → (3, −2).

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Reflect across the x-axis

Reflecting across the x-axis flips the sign of y.

(3, 2)⇒(3, −2)(3,\, 2) \Rightarrow (3,\, -2)
02 / YOUR TURN

Practice until it feels automatic.

Your turn

Work it out.

Type (x, y), e.g. (3, -2).

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Your answer:
— / WHY IT WORKS

The idea underneath.

Flip one sign

A reflection over the x-axis keeps x and negates y; over the y-axis keeps y and negates x.

Why it works

Mirror across the axis.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

Reflect (4,4) across the x-axis.

1

Reflect across the x-axis

Reflecting across the x-axis flips the sign of y. (4, 4) ⇒ (4, -4)

EX 2medium

Reflect (-4,4) across the y-axis.

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Reflect across the y-axis

Reflecting across the y-axis flips the sign of x. (-4, 4) ⇒ (4, 4)

EX 3hard

Reflect (-3,-1) across the x-axis.

1

Reflect across the x-axis

Reflecting across the x-axis flips the sign of y. (-3, -1) ⇒ (-3, 1)

04 / COMMON TRAPS

Where students slip.

Trap

Flipping the wrong coordinate.

Fix

x-axis reflection changes y, not x.

Trap

Flipping both signs.

Fix

Reflect over one axis changes only one sign.

05 / QUIZ

Test yourself.

The Test

12 problems across three tiers. Auto-graded on submit. Hints and a full walkthrough on every question. Your work is saved on this device — sign in to keep it across devices.

0/12Answered
How to answerType just the value. Formatting won't trip you up — we ignore spaces, capital letters, commas, and subscript style, so t₁ = 5, d = 3 and t1=5,d=3 both count. For a list of numbers, separate them with commas (e.g. 3, 10, 17).
Core

Core (4)

C1

Reflect (6,1) across the x-axis.

Need a hint?
  • Across the x-axis → change y’s sign.
  • Across the y-axis → change x’s sign.
C2

Reflect (6,-1) across the x-axis.

Need a hint?
  • Across the x-axis → change y’s sign.
  • Across the y-axis → change x’s sign.
C3

Reflect (-2,6) across the y-axis.

Need a hint?
  • Across the x-axis → change y’s sign.
  • Across the y-axis → change x’s sign.
C4

Reflect (6,-2) across the x-axis.

Need a hint?
  • Across the x-axis → change y’s sign.
  • Across the y-axis → change x’s sign.
Apply

Apply (4)

A1

Reflect (2,-5) across the x-axis.

Need a hint?
  • Across the x-axis → change y’s sign.
  • Across the y-axis → change x’s sign.
A2

Reflect (4,-6) across the y-axis.

Need a hint?
  • Across the x-axis → change y’s sign.
  • Across the y-axis → change x’s sign.
A3

Reflect (6,-2) across the x-axis.

Need a hint?
  • Across the x-axis → change y’s sign.
  • Across the y-axis → change x’s sign.
A4

Reflect (6,6) across the y-axis.

Need a hint?
  • Across the x-axis → change y’s sign.
  • Across the y-axis → change x’s sign.
Extension

Extension (4)

E1

Reflect (-1,-4) across the x-axis.

Need a hint?
  • Across the x-axis → change y’s sign.
  • Across the y-axis → change x’s sign.
E2

Reflect (5,4) across the y-axis.

Need a hint?
  • Across the x-axis → change y’s sign.
  • Across the y-axis → change x’s sign.
E3

Reflect (3,-3) across the y-axis.

Need a hint?
  • Across the x-axis → change y’s sign.
  • Across the y-axis → change x’s sign.
E4

Reflect (2,-4) across the x-axis.

Need a hint?
  • Across the x-axis → change y’s sign.
  • Across the y-axis → change x’s sign.