Question

The parallelogram on the left was dilated by a scale factor of 2 about point P. It was then transformed in another way to produce the parallelogram on the right.

Which identifies the transformation that occurred after the dilation?
a translation of 9 units to the right
a translation of 3 units down
a reflection across the x-axis
a reflection across the y-axis

Answer 1

the answer is A. a translation of 9 units to the right

Answer 2

The correct option is A.

Explanation:

From the given figure it is noticed that the vertices of left figure are (-2,0), (-4,0), (-3,-3), (-5,-3). The vertices of right figure are (3,0), (7,0), (1,-6), (5,-6).

Dilated by a scale factor of 2 about point P.

`(x,y)\rightarrow (2(x+2)-2,2y)`

The coordinates after dilation are (-2,0), (-6,0), (-4,-6), (-8,-6).

The point P' is 9 unit right from the point P. therefore the second step is a translation of 9 units to the right. After translation,

`(x,y)\rightarrow (x+9,y)`

The coordinates after translation are (3,0), (7,0), (1,-6), (5,-6).

Therefore option A is correct.