Question

graph the image of kite tuvw after a dilation with a scale factor of \\(\frac{1}{4}\\), centered at the origin.

Explanation:

Step1: Identify original coordinates

From graph: $T(4,-8)$, $U(8,0)$, $V(4,8)$, $W(-8,0)$

Step2: Apply dilation rule

Multiply each coordinate by $\frac{1}{4}$:
$T'(4\times\frac{1}{4}, -8\times\frac{1}{4})=(1,-2)$
$U'(8\times\frac{1}{4}, 0\times\frac{1}{4})=(2,0)$
$V'(4\times\frac{1}{4}, 8\times\frac{1}{4})=(1,2)$
$W'(-8\times\frac{1}{4}, 0\times\frac{1}{4})=(-2,0)$

Step3: Graph the image

Plot $T'(1,-2)$, $U'(2,0)$, $V'(1,2)$, $W'(-2,0)$ and connect them.

Answer:

The image of kite TUVW after dilation has vertices at $(1,-2)$, $(2,0)$, $(1,2)$, and $(-2,0)$. (Plot these points to form the dilated kite.)