Question

The coordinates of triangle QRS are Q(-2, 4), R14,0) and S(6,2). The figure was dilated and the new coordinates are Q(-3, 6), R'(6,0) and S'(9,3). What is the scale factor? What is the algebraic rule?​

Answer 1

Scale factor is 3/2

Explanation:

Just take any coordinate of any point that was scaled and that had a non-zero initial value. Let’s take the x axis of Q. There’s
`x_Q = -2 \land x_(Q') = -3`.

So, the scaling factor has to be
`(x_(Q'))/(x_Q) = (-3)/(-2) = (3)/(2)`. You can confirm that
`(x_(Q'))/(x_Q) = (y_(Q'))/(y_Q) = (x_(R'))/(x_R) = (x_(S'))/(x_S) = (y_(S'))/(y_S)`. (I omitted
`(y_(R'))/(y_R)` because of zero values)

The algebraic rule for getting the point
`P'(x_(P'), y_(P'))` in the dilated space from any given point
`P(x_P, y_P)` is
`\left \{ {{x_(P') = (3)/(2)x_P} \atop {y_(P') = (3)/(2)y_P}} \right.`