Question

on a separate sheet of paper, graph the image of △fgh with the given vertices after a dilation centered at the origin with the given scale factor. what are the coordinates of the vertices of the image? write your answers as decimals, if necessary. f(-10, 4), g(-4, 4), h(-4, -8), k = 0.25

Explanation:

Step1: Recall dilation formula

For a dilation centered at the origin with scale - factor $k$, if a point $(x,y)$ is dilated, the new point $(x',y')$ is given by $(x',y')=(k\cdot x,k\cdot y)$.

Step2: Find the new coordinates of point $F$

Given $F(-10,4)$ and $k = 0.25$.
$x_F'=0.25\times(-10)=- 2.5$
$y_F'=0.25\times4 = 1$

Step3: Find the new coordinates of point $G$

Given $G(-4,4)$ and $k = 0.25$.
$x_G'=0.25\times(-4)=-1$
$y_G'=0.25\times4 = 1$

Step4: Find the new coordinates of point $H$

Given $H(-4,-8)$ and $k = 0.25$.
$x_H'=0.25\times(-4)=-1$
$y_H'=0.25\times(-8)=-2$

Answer:

$F(-2.5,1)$
$G(-1,1)$
$H(-1,-2)$