Question

graph the polygon with the given vertices and its image after a dilation with scale factor k. q(-3,-2), r(1,2), s(4,1); k = 4

Explanation:

Step1: Apply the dilation formula

The formula for dilation is \((x,y)\to(kx,ky)\) where \(k = 4\).
For point \(Q(-3,-2)\):
\(x=-3,y = - 2,k = 4\)
\(Q'=(4\times(-3),4\times(-2))=(-12,-8)\)

Step2: Calculate the image of point \(R\)

For point \(R(1,2)\):
\(x = 1,y=2,k = 4\)
\(R'=(4\times1,4\times2)=(4,8)\)

Step3: Calculate the image of point \(S\)

For point \(S(4,1)\):
\(x = 4,y = 1,k = 4\)
\(S'=(4\times4,4\times1)=(16,4)\)

Answer:

Plot the original polygon with vertices \(Q(-3,-2)\), \(R(1,2)\), \(S(4,1)\) and the dilated polygon with vertices \(Q'(-12,-8)\), \(R'(4,8)\), \(S'(16,4)\) on the given coordinate - grid.