Task Sets: Verify dilation properties - Common Core Math - HS Geometry

Fluency Practice

Apply the properties of dilations directly. Show your reasoning.

$Coordinate plane showing triangle ABC and its dilation A'B'C' with center at the origin and scale factor 2. Dashed rays connect the center through each pair of corresponding vertices.$

Triangle $ABC$ has vertices $A(1, 1)$ , $B(3, 1)$ , and $C(1, 3)$ . A dilation with center $O(0, 0)$ and scale factor $k = 2$ maps each vertex to $A' = (2, 2)$ , $B' = (6, 2)$ , and $C' = (2, 6)$ . What is the length of side $A'B'$ ?

A dilation has center $C$ and scale factor $k = 0.5$ . Point $P$ is 8 units from $C$ . After the dilation, how far is $P'$ from $C$ ?

16 units — the image is farther from the center.

4 units — the image is half as far from the center.

8 units — the center and image stay the same distance apart.

0.5 units — the scale factor is subtracted from the distance.

$Two parallel lines with slope 2. The original line ell is closer to center C; the image line ell-prime is farther, shifted by the dilation but maintaining the same slope.$

Line $\ell$ has slope $2$ and does not pass through center $C$ . After a dilation with center $C$ and scale factor $k = 3$ , what is the slope of the image line $\ell'$ ?

Line $m$ passes through the center $C$ of a dilation with scale factor $k = 5$ . After the dilation, which best describes the image of line $m$ ?

The image is a new line parallel to $m$ .

The image is a new line perpendicular to $m$ .

The image is the same line $m$ — the line is unchanged.

The image does not exist because lines through the center are fixed points.

Segment $PQ$ has length 9 cm. It is dilated with scale factor $k = \frac{2}{3}$ . What is the length of the image segment $P'Q'$ in centimeters?

Exercises: Properties of Dilations

Warm-Up: Review What You Know

Fluency Practice