Question

the figure below is dilated by a factor of 4 centered at the origin. plot the resulting image. click twice to plot a segment. click a segment to delete it.

Explanation:

Step1: Find coordinates of original points

Assume the coordinates of points \(P(-1,-1)\), \(Q(0,-2)\), \(R(2,0)\), \(S(0,2)\), \(T(-1,2)\)

Step2: Apply dilation formula

The dilation formula centered at the origin is \((x,y)\to(kx,ky)\), where \(k = 4\).
For point \(P(-1,-1)\): \((-1\times4,-1\times4)=(-4,-4)\)
For point \(Q(0,-2)\): \((0\times4,-2\times4)=(0,-8)\)
For point \(R(2,0)\): \((2\times4,0\times4)=(8,0)\)
For point \(S(0,2)\): \((0\times4,2\times4)=(0,8)\)
For point \(T(-1,2)\): \((-1\times4,2\times4)=(-4,8)\)

Answer:

Plot the points \((-4,-4)\), \((0,-8)\), \((8,0)\), \((0,8)\), \((-4,8)\) and connect them to form the dilated figure.