Question

△rst has vertices r(-5, 1), s(-3, 4), and t(2, -1), and is dilated by k = 2 from the origin, (0, 0) or do. determine the coordinates of △rst. r( ) s( ) t( )

Explanation:

Step1: Recall dilation formula

When a point $(x,y)$ is dilated by a scale - factor $k$ from the origin $(0,0)$, the new coordinates $(x',y')$ are given by $(x',y')=(k\cdot x,k\cdot y)$.

Step2: Find coordinates of $R'$

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

Step3: Find coordinates of $S'$

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

Step4: Find coordinates of $T'$

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

Answer:

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