Question

△rst is dilated with the rule $d_{t,1/3} (x, y)$, where the center of dilation is t(3, −2).
the distance between the x-coordinates of r and t is
the distance between the y-coordinates of r and t is
r is from t, so the coordinates of r are .

Explanation:

Step1: Find coordinates of R

From graph: R(0,4), T(3,-2)

Step2: Calculate x-distance

$|0 - 3| = 3$

Step3: Calculate y-distance

$|4 - (-2)| = 6$

Step4: Determine R' position

Dilation factor $\frac{1}{3}$: R' is $\frac{1}{3}$ the distance from T

Step5: Compute R' coordinates

x: $3 + \frac{1}{3}(0 - 3) = 3 - 1 = 2$
y: $-2 + \frac{1}{3}(4 - (-2)) = -2 + 2 = 0$

Answer:

3
6
1/3 the distance
(2, 0)