Question

1. triangle rst below will be dilated with the origin as the center of dilation and a scale factor of 4. what will be the coordinates of the vertices of the dilated image, △rst? a. r(4,12),s(12,12),t(8,4) b. r(4,12),s(9,9),t(8,1) c. r(2,6),s(12,12),t(4,2) d. r(1/4,3/4),s(1/2,1/4),t(1,5/4)

Explanation:

Step1: Identify original coordinates

From the graph, the coordinates of $\triangle RST$ are $R(1,3)$, $S(3,3)$, $T(2,1)$.

Step2: Apply dilation formula

When dilating a point $(x,y)$ with the origin as the center of dilation and a scale - factor $k$, the new coordinates $(x',y')$ are given by $(x',y')=(k\times x,k\times y)$. Here $k = 4$.
For point $R(1,3)$: $R'=(4\times1,4\times3)=(4,12)$.
For point $S(3,3)$: $S'=(4\times3,4\times3)=(12,12)$.
For point $T(2,1)$: $T'=(4\times2,4\times1)=(8,4)$.

Answer:

A. $R'(4,12),S'(12,12),T'(8,4)$