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 the coordinates of original points

Assume \(N=(0,0)\), \(P=(2,0)\), \(Q=(0,2)\), \(R = (- 2,1)\), \(O=(1,-1)\)

Step2: Apply the dilation formula

The dilation formula centered at the origin \((x,y)\to(kx,ky)\) where \(k = 4\)

• For \(P(2,0)\): \((2\times4,0\times4)=(8,0)\)
• For \(Q(0,2)\): \((0\times4,2\times4)=(0,8)\)
• For \(R(-2,1)\): \((-2\times4,1\times4)=(-8,4)\)
• For \(O(1,-1)\): \((1\times4,-1\times4)=(4,-4)\)
• \(N(0,0)\) remains \((0,0)\) since \(0\times4 = 0\)

Answer:

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