Question

1. dilate △abc to form △def using the origin (0, 0) as the center of dilation and a scale factor of 2.

Explanation:

Step1: Identify the coordinates of △ABC

Assume \(A=(2,2)\), \(B=(2,10)\), \(C=(6,2)\)

Step2: Apply the dilation formula

The dilation formula with center at the origin \((0,0)\) and scale - factor \(k = 2\) is \((x,y)\to(kx,ky)\)
For point \(A=(2,2)\), after dilation \(D=(2\times2,2\times2)=(4,4)\)
For point \(B=(2,10)\), after dilation \(E=(2\times2,2\times10)=(4,20)\)
For point \(C=(6,2)\), after dilation \(F=(2\times6,2\times2)=(12,4)\)

Step3: Plot the new triangle △DEF

Plot the points \(D(4,4)\), \(E(4,20)\), \(F(12,4)\) and connect them to form △DEF

Answer:

The coordinates of the vertices of △DEF are \(D(4,4)\), \(E(4,20)\), \(F(12,4)\)