Question

graph and label each figure and its image under a dilation with the given scale factor. assume all dilations use the origin as the center of dilation.

1. triangle rst with vertices r(-5, 1), s(-3, 4), and t(2, -1): ( k = 2 )
2. rectangle abcd with vertices a(-3, 0), b(1, 2), c(2, 0), and d(-2, -2): ( k = 3 )

Explanation:

Step1: Dilate triangle vertices (k=2)

For a dilation with center at origin, multiply each coordinate by scale factor $k$.
$R' = (-5 \times 2, 1 \times 2) = (-10, 2)$
$S' = (-3 \times 2, 4 \times 2) = (-6, 8)$
$T' = (2 \times 2, -1 \times 2) = (4, -2)$

Step2: Dilate rectangle vertices (k=3)

Multiply each coordinate of rectangle vertices by scale factor $k$.
$A' = (-3 \times 3, 0 \times 3) = (-9, 0)$
$B' = (1 \times 3, 2 \times 3) = (3, 6)$
$C' = (2 \times 3, 0 \times 3) = (6, 0)$
$D' = (-2 \times 3, -2 \times 3) = (-6, -6)$

Answer:

1. Triangle RST image vertices:

$R': (-10, 2)$, $S': (-6, 8)$, $T': (4, -2)$

1. Rectangle ABCD image vertices:

$A': (-9, 0)$, $B': (3, 6)$, $C': (6, 0)$, $D': (-6, -6)$

(To complete the task, plot these new points on their respective grids and connect them to form the dilated figures, labeling each vertex.)