Question

graph the image of kite abcd after a dilation with a scale factor of 5, centered at the origin.

Explanation:

Step1: Recall dilation rule

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 $(x',y')=(k\cdot x,k\cdot y)$. Here $k = 5$.

Step2: Find coordinates of dilated points

• Point $A(0, - 2)$: After dilation, $A'(0\times5,-2\times5)=(0,-10)$.
• Point $B(2,0)$: After dilation, $B'(2\times5,0\times5)=(10,0)$.
• Point $C(0,2)$: After dilation, $C'(0\times5,2\times5)=(0,10)$.
• Point $D(-2,0)$: After dilation, $D'(-2\times5,0\times5)=(-10,0)$.

Step3: Graph the new kite

Plot the points $A'(0, - 10)$, $B'(10,0)$, $C'(0,10)$ and $D'(-10,0)$ on the coordinate - plane and connect them in order to form the dilated kite.

Answer:

Plot the points $A'(0,-10)$, $B'(10,0)$, $C'(0,10)$ and $D'(-10,0)$ and connect them to get the dilated kite.