Question

dilate △fgh by a scale factor of 4 with the center of dilation at the origin. graph the dilation.

Explanation:

Step1: Find coordinates of original points

Assume \(G=(0,0)\), \(P = (-1,0)\), \(H=(-1,-2)\)

Step2: Apply dilation formula

For a dilation with scale factor \(k = 4\) and center at the origin \((x,y)\to(kx,ky)\)

• For \(G=(0,0)\): \(4\times0 = 0\), \(4\times0=0\), new \(G'=(0,0)\)
• For \(P=(-1,0)\): \(4\times(-1)=-4\), \(4\times0 = 0\), new \(P'=(-4,0)\)
• For \(H=(-1,-2)\): \(4\times(-1)=-4\), \(4\times(-2)=-8\), new \(H'=(-4,-8)\)

Answer:

Plot the points \(G'(0,0)\), \(P'(-4,0)\) and \(H'(-4,-8)\) and connect them to form the dilated triangle \(\triangle F'G'H'\) (where \(F'\) is part of the dilated figure).