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.

On a coordinate plane, parallelogram P has points (negative 4, 0), (negative 2, 0), (negative 3, negative 3), (negative 5, negative 3). Parallelogram P prime has points (3, 0), (7, 0), (5, negative 6), (1, negative 6).
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 for 20 points thx:}

Answer 1

The correct answer is: a translation of 3 units down.

Explanation:

To identify the transformation that occurred after the dilation, we can compare corresponding points on both parallelograms.

The point (-4,0) on parallelogram P was dilated to the point (3,0) on parallelogram P'. This means the x-coordinate was multiplied by 2, since 3 = -4 x 2.

Similarly, the point (-2,0) on parallelogram P was dilated to the point (7,0) on parallelogram P', indicating again that the x-coordinate was multiplied by 2 since 7 = -2 x 2.

Therefore, the dilation was a scale factor of 2 in the x-direction about point P.

To transform parallelogram P' from its position after the dilation to its final position, we can see that corresponding points have been translated 3 units down. For example, the point (3,0) was transformed to (3,-3), and the point (1,-6) was transformed to (-4,-6).

Thus, the transformation that occurred after the dilation was a translation of 3 units down.

Therefore, the correct answer is: a translation of 3 units down.