Question

rectangle efgh has the ordered pairs e(-2, 2), f(0, 2), g(0, -2), and h(-2, -2). dilate rectangle efgh by a scale factor of 2 with the center as the origin. e f g h what are the coordinates for e, f, g and h type your answer here

Explanation:

Step1: Recall dilation formula

When dilating a point $(x,y)$ by a scale factor $k$ with the center of dilation at the origin $(0,0)$, the new - point $(x',y')$ is given by $(x',y')=(k\times x,k\times y)$.

Step2: Find coordinates of $E'$

For point $E(-2,2)$ and $k = 3$, we have $x=-2$ and $y = 2$. Then $x'=3\times(-2)=-6$ and $y'=3\times2 = 6$. So $E'(-6,6)$.

Step3: Find coordinates of $F'$

For point $F(0,2)$ and $k = 3$, we have $x = 0$ and $y = 2$. Then $x'=3\times0=0$ and $y'=3\times2 = 6$. So $F'(0,6)$.

Step4: Find coordinates of $G'$

For point $G(0,-2)$ and $k = 3$, we have $x = 0$ and $y=-2$. Then $x'=3\times0=0$ and $y'=3\times(-2)=-6$. So $G'(0,-6)$.

Step5: Find coordinates of $H'$

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

Answer:

$E'(-6,6)$
$F'(0,6)$
$G'(0,-6)$
$H'(-6,-6)$