Question

triangle rst with vertices r(-5, 1), s(-3, 4), and t(2, -1); k = 2

Explanation:

Step1: Recall dilation formula

To dilate a point $(x,y)$ by a scale - factor $k$, the new coordinates $(x',y')$ are given by $(x',y')=(k\cdot x,k\cdot y)$.

Step2: Find new coordinates of point R

For point $R(-5,1)$ with $k = 2$, we have $x=-5$ and $y = 1$. Then $x'=2\times(-5)=-10$ and $y'=2\times1 = 2$. So $R'(-10,2)$.

Step3: Find new coordinates of point S

For point $S(-3,4)$ with $k = 2$, we have $x=-3$ and $y = 4$. Then $x'=2\times(-3)=-6$ and $y'=2\times4 = 8$. So $S'(-6,8)$.

Step4: Find new coordinates of point T

For point $T(2,-1)$ with $k = 2$, we have $x = 2$ and $y=-1$. Then $x'=2\times2 = 4$ and $y'=2\times(-1)=-2$. So $T'(4,-2)$.

Answer:

The vertices of the dilated triangle are $R'(-10,2)$, $S'(-6,8)$, $T'(4,-2)$