Question

graph the image of kite abcd after a dilation with a scale factor of 4, centered at the origin.

Explanation:

Step1: Identify original coordinates

Original vertices: $A(0,-2)$, $B(2,1)$, $C(0,2)$, $D(-2,1)$

Step2: Apply dilation rule

For dilation centered at origin with scale factor $k=4$, new coordinate $(x',y')=(4x,4y)$:

• $A'(0\times4, -2\times4)=(0,-8)$
• $B'(2\times4, 1\times4)=(8,4)$
• $C'(0\times4, 2\times4)=(0,8)$
• $D'(-2\times4, 1\times4)=(-8,4)$

Step3: Plot new vertices

Plot $A'(0,-8)$, $B'(8,4)$, $C'(0,8)$, $D'(-8,4)$ and connect to form the dilated kite.

Answer:

The vertices of the dilated kite are $A'(0,-8)$, $B'(8,4)$, $C'(0,8)$, $D'(-8,4)$. When plotted and connected, these form the image of kite $ABCD$ after dilation with scale factor 4 centered at the origin.