geometry (please explain)

Question

Triangle MNO and triangle PQR are shown on the coordinate plane.

What sequence of transformations proves ΔMNO ~ ΔPQR?

 A. ΔMNO was dilated by a factor of 3 about the origin, then reflected across the x-axis to form ΔPQR. 

B. ΔMNO was dilated by a factor of 3 about from the origin, then reflected across the y-axis to form ΔPQR.

C.  ΔMNO was dilated by a factor of 4 about the origin, then rotated 180° clockwise about the origin to form ΔPQR. 

D. ΔMNO was dilated by a factor of 4 about the origin, then translated left 7 units to form ΔPQR.

Answer 1

Obviously, ΔPQR is larger than ΔMNO so (if they're similar) then a dilation must be involved. And we see all the answers start with a dilation. To determine the amount of the dilation, you can look at any of the sides and see how much bigger they are. Notice on ΔMNO, side MN is 2 units long? The side the corresponds to that in ΔPDR is PQ and it is 6 units long. Since 6/2 = 3, ΔPQR is 3 times bigger. You could check the other sides to make sure they are also 3 times bigger if you wanted.

Notice which direction ΔMNO is reflected? It is reflected across the y-axis.