Question

1). rectangle abcd with vertices a(-3,0), b(1,2), c(2,0), and d(-2,-2): k = 3

Explanation:

Step1: Recall dilation formula

For a point $(x,y)$ dilated by a scale - factor $k$ about the origin, the new point $(x',y')$ is given by $(x',y')=(k x,k y)$.

Step2: Dilate point A

For point $A(-3,0)$ with $k = 3$, we have $x=-3,y = 0$. Then $x'=3\times(-3)=-9$ and $y'=3\times0 = 0$. So $A'(-9,0)$.

Step3: Dilate point B

For point $B(1,2)$ with $k = 3$, we have $x = 1,y = 2$. Then $x'=3\times1=3$ and $y'=3\times2 = 6$. So $B'(3,6)$.

Step4: Dilate point C

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

Step5: Dilate point D

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

Answer:

The vertices of the dilated rectangle are $A'(-9,0),B'(3,6),C'(6,0),D'(-6,-6)$