Question

Triangle ABC has Points A, B, and C located at (3,6), (-2,-2) and (6,4), respectively. triangle ABC’s dilated image A’B’C’ has a Point of A’ located at (1,2). What is the scale factor

Answer 1

Triangle ABC has its vertices at points A(3,6), B(-2,-2), and C(6,4)

This triangle was dilated and triangle A'B'C' was determined. The coordinates of one of the vertices of the dilated triangle are A'(1,2)

To perform the dilation, the coordinates of each vertex of the triangle were multiplied by a scale factor "k" following the rule:

`(x,y)\to(kx,ky)`

Compare the coordinates of the corresponding points A and A' to determine the scale factor used in the dilation:

x-coordinate of A is 3

x-coordinate of A' is 1

Then:

`\begin{gathered} kx_A=x_(A^(\prime)) \\ 3k=1 \\ (3k)/(3)=(1)/(3) \\ k=(1)/(3) \end{gathered}`

The scale factor used is k=1/3