Question

write the coordinates of the vertices after a dilation with a scale factor of $\frac{1}{3}$, centered at the origin.

Explanation:

Step1: Identify original coordinates

$A(-9, - 9)$, $B(3,-9)$, $C(3,6)$, $D(-9,6)$

Step2: Apply dilation formula

For a dilation centered at the origin with scale - factor $k=\frac{1}{3}$, if a point has coordinates $(x,y)$, its new coordinates $(x',y')$ are given by $(x',y')=(k x,k y)$.
For point $A$: $x'_A=\frac{1}{3}\times(-9)=- 3$, $y'_A=\frac{1}{3}\times(-9)=-3$
For point $B$: $x'_B=\frac{1}{3}\times3 = 1$, $y'_B=\frac{1}{3}\times(-9)=-3$
For point $C$: $x'_C=\frac{1}{3}\times3 = 1$, $y'_C=\frac{1}{3}\times6 = 2$
For point $D$: $x'_D=\frac{1}{3}\times(-9)=-3$, $y'_D=\frac{1}{3}\times6 = 2$

Answer:

$A'(-3,-3)$, $B'(1,-3)$, $C'(1,2)$, $D'(-3,2)$