Question

1. triangle abc has vertices a(1,6), b(5,4), and c(3,1). triangle abc will be dilated by a scale factor of 3, with the center of dilation at the origin. a. find the coordinates of the vertices of the dilated image, △abc. show your work. b. on the coordinate grid, graph △abc and its image, △abc.

Explanation:

Step1: Recall dilation formula

For a dilation with scale - factor \(k\) centered at the origin \((0,0)\), the transformation rule for a point \((x,y)\) is \((x,y)\to(kx,ky)\). Here \(k = 3\).

Step2: Find coordinates of \(A'\)

Given \(A(1,6)\), using the dilation formula \((x,y)\to(kx,ky)\) with \(k = 3\), we have \(A'(3\times1,3\times6)=A'(3,18)\).

Step3: Find coordinates of \(B'\)

Given \(B(5,4)\), using the dilation formula \((x,y)\to(kx,ky)\) with \(k = 3\), we have \(B'(3\times5,3\times4)=B'(15,12)\).

Step4: Find coordinates of \(C'\)

Given \(C(3,1)\), using the dilation formula \((x,y)\to(kx,ky)\) with \(k = 3\), we have \(C'(3\times3,3\times1)=C'(9,3)\).

Answer:

The coordinates of \(\triangle A'B'C'\) are \(A'(3,18)\), \(B'(15,12)\), \(C'(9,3)\)