Transformations

A transformation moves a shape. Translations slide, reflections flip, and rotations turn. These three keep the size and shape. Dilations resize.

A reflection flips a shape across a line. Each point lands the same distance on the other side.

Move	Rule
Reflect in the $x$ -axis	$(x, y) \to (x, - y)$
Reflect in the $y$ -axis	$(x, y) \to (- x, y)$
Rotate $9 0^{\circ}$ counterclockwise	$(x, y) \to (- y, x)$
Rotate $18 0^{\circ}$	$(x, y) \to (- x, - y)$
Dilate by $k$	$(x, y) \to (k x, k y)$

Work through it

Right adds to $x$ , up adds to $y$ . $(5, 3)$

Use $(x, y) \to (- y, x)$ . $(- 1, 3)$

Reflecting in the $x$ -axis and changing $x$ .

Across the $x$ -axis, the point moves up or down, so $y$ changes.

The short version
Translate: add to the coordinates. Reflect across

x

-axis: negate

y

. Across

y

-axis: negate

x

. Rotate

9 0^{\circ}

counterclockwise:

(x, y) \to (- y, x)