Before you read

Answer first — see what you already know.

What is the image of $(4, - 3)$ after reflection over the x-axis?

A
$(4, 3)$
B
$(- 4, - 3)$
C
$(- 4, 3)$
D
$(3, - 4)$

Check your answer

Answer:

Before you read

Answer first — see what you already know.

Rotate $(2, 5)$ by $180°$ about the origin.

A
$(- 2, - 5)$
B
$(5, 2)$
C
$(- 5, 2)$
D
$(2, - 5)$

Check your answer

Answer:

Theory

The Four Transformations

Translation (slide): $(x, y) \to (x + a, y + b)$

Translation by (3,2): (x,y) → (x+3, y+2)

Reflection:
- Over x-axis: $(x, y) \to (x, -y)$
- Over y-axis: $(x, y) \to (-x, y)$
- Over $y = x$ : $(x, y) \to (y, x)$

Reflection over the y-axis: (x,y) → (−x,y)

Rotation about the origin:
- $90°$ counterclockwise: $(x, y) \to (-y, x)$
- $180°$ : $(x, y) \to (-x, -y)$
- $270°$ counterclockwise (or $90°$ clockwise): $(x, y) \to (y, -x)$

Dilation with scale factor $k$ from origin: $(x, y) \to (kx, ky)$

Dilation with scale factor 2 from the origin

Example 1

Reflect $(3, -5)$ over the y-axis, then translate by $(2, 1)$ .

Reflect over y-axis: $(-3, -5)$

Translate: $(-3+2, -5+1) = (-1, -4)$

(-1, -4)

Tip

ACT Pro Tip

Memorize the reflection rules. The ACT's favorite: reflection over the x-axis (negate $y$ ) and over the y-axis (negate $x$ ). For $180°$ rotation, just negate both coordinates.

Ready to ace the SAT?

Try NovaMath free — AI tutoring, 115 lessons, 2,400+ exercises.

Try NovaMath Free