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 1

A translation of 9 units to the right

Explanation:

Answer 2

A translation of 9 units to the right

Explanation:

See the attached figure.

The parallelogram on the left (green parallelogram ) was dilated by a scale factor of 2 about point P.

The points of the green parallelogram (-4, 0), (-2, 0), (-3, -3), (-5, -3).

The result of dilation will be the dot black parallelogram.

The points of the dot black parallelogram (-6, 0), (-2, 0), (-4, -6), (-8, -6).

The dot black parallelogram then transformed in another way to produce the parallelogram on the right (red parallelogram)

The points of the red parallelogram (3, 0), (7, 0), (5, -6), (1, -6).

It is required to find the transformation rule that occurred after the dilation.

The dot black parallelogram → the red parallelogram

(-6,0) →(3,0) ⇒ (x,y)→(x+h , y+k)

x = -6 , x+h = 3 ⇒ h=3-x = 3-(-6) = 9

y = 0 , y+k = 0 ⇒ k = 0

The transformation rule is (x,y)→( x+9 , y )

Which mean a translation of 9 units to the right