Question

dilate \\( \triangle fgh \\) by a scale factor of 4 with the center of dilation at the origin.
graph the dilation.

Explanation:

Step1: Find coordinates of original triangle

From the graph, assume \(F(-1, -1)\), \(G(0, -1)\), \(H(-1, -2)\) (approximate based on grid).

Step2: Apply dilation formula

The dilation formula with center at origin \((x,y)\to(kx,ky)\), where \(k = 4\).
For \(F(-1,-1)\): \((-1\times4,-1\times4)=(-4,-4)\)
For \(G(0,-1)\): \((0\times4,-1\times4)=(0,-4)\)
For \(H(-1,-2)\): \((-1\times4,-2\times4)=(-4,-8)\)

Answer:

Plot the points \(F'(-4,-4)\), \(G'(0,-4)\), \(H'(-4,-8)\) and connect them to form the dilated triangle \(\triangle F'G'H'\).