Question

1. graph the triangle and its image after a dilation with scale factor k.

p(2,2), q(4,4), r(8,2); k = 1/2

Explanation:

Step1: Apply dilation formula

For a point \((x,y)\) and scale factor \(k\), the image after dilation is \((kx,ky)\).

Step2: Find image of \(P(2,2)\)

For \(P(2,2)\) with \(k = \frac{1}{2}\), \(P'(2\times\frac{1}{2},2\times\frac{1}{2})=(1,1)\).

Step3: Find image of \(Q(4,4)\)

For \(Q(4,4)\) with \(k=\frac{1}{2}\), \(Q'(4\times\frac{1}{2},4\times\frac{1}{2})=(2,2)\).

Step4: Find image of \(R(8,2)\)

For \(R(8,2)\) with \(k = \frac{1}{2}\), \(R'(8\times\frac{1}{2},2\times\frac{1}{2})=(4,1)\).

Answer:

Plot the original triangle with vertices \(P(2,2)\), \(Q(4,4)\), \(R(8,2)\) and the dilated triangle with vertices \(P'(1,1)\), \(Q'(2,2)\), \(R'(4,1)\) on the coordinate plane.