Question

1. graph the image of $\triangle fgh$ after a dilation with a scale factor of 2, centered at the origin.

Explanation:

Step1: Identify original coordinates

Original vertices: $F(-4, 4)$, $G(1, 4)$, $H(-3, -5)$

Step2: Apply dilation formula

For dilation centered at origin with scale factor $k=2$, use $(x,y)\to(kx,ky)$

• $F'$: $(-4\times2, 4\times2)=(-8, 8)$
• $G'$: $(1\times2, 4\times2)=(2, 8)$
• $H'$: $(-3\times2, -5\times2)=(-6, -10)$

Step3: Plot new vertices

Plot $F'(-8,8)$, $G'(2,8)$, $H'(-6,-10)$ and connect them.

Answer:

The vertices of the dilated triangle $\Delta F'G'H'$ are $F'(-8, 8)$, $G'(2, 8)$, and $H'(-6, -10)$. When plotted and connected, these form the image of $\Delta FGH$ after the dilation.