Question

graph the polygon with the given vertices and its image after a dilation with scale factor k
l(0, 0), m(-4, 1), n(-3, -6); k = -3

Explanation:

Step1: Recall dilation rule

To dilate a point \((x,y)\) with scale factor \(k\), the new point is \((kx,ky)\).

Step2: Dilate point \(L(0,0)\)

For \(L(0,0)\) and \(k = - 3\), we have \(L'=(-3\times0,-3\times0)=(0,0)\).

Step3: Dilate point \(M(-4,1)\)

For \(M(-4,1)\) and \(k=-3\), we calculate \(M'=(-3\times(-4),-3\times1)=(12, - 3)\).

Step4: Dilate point \(N(-3,-6)\)

For \(N(-3,-6)\) and \(k = - 3\), we calculate \(N'=(-3\times(-3),-3\times(-6))=(9,18)\).

Answer:

The vertices of the image after dilation are \(L'(0,0)\), \(M'(12,-3)\), \(N'(9,18)\). To graph the original polygon, plot \(L(0,0)\), \(M(-4,1)\), \(N(-3,-6)\) and connect them. To graph the image, plot \(L'(0,0)\), \(M'(12,-3)\), \(N'(9,18)\) and connect them.