The vertices of ∆MNO and ∆PQR are described in the table. How can ∆MNO ~ ∆PQR be justified using rigid and non-rigid transformations?

Question

The vertices of ∆MNO and ∆PQR are described in the table.

∆MNO∆PQR
M (2, 4)	P (−4, 8)
N (5, 4)	Q (−10, 8)
O (6, 2)	R (−12, 4)

How can ∆MNO ~ ∆PQR be justified using rigid and non-rigid transformations? 

1. ∆MNO was dilated by a scale factor of  from the origin, then rotated 180° clockwise about the origin to form ∆PQR. 
2. ∆MNO was dilated by a scale factor of  from the origin, then reflected over the x-axis to form ∆PQR.
3. ∆MNO was dilated by a scale factor of 2 from the origin, then reflected over the y-axis to form ∆PQR. 
4. ∆MNO was dilated by a scale factor of 2 from the origin, then translated left 5 units to form ∆PQR.

Answer 1

The correct answer is choice 3.

A dilation by a factor of 2 doubles the x- and y-values, and thus yields:

(4,8)

(10,8)

(12,4)

A reflection over the y-axis leaves the y-values alone and changes the signs of the x-values:

(-4,8)

(-10,8)

(-12,4)