Question

Quadrilateral ABCD underwent a sequence of transformations to give quadrilateral A′B′C′D′. Which transformations could have taken place?

A) a reflection across the x-axis followed by a reflection across the y-axis

B) a translation 10 units down followed by a translation 8 units to the right

C) a rotation 90° counterclockwise about the origin followed by a reflection across the y-axis

D) a reflection across the line y = x followed by a reflection across the line y = -x

Answer 1

A translation is just like sliding the figure across the plane. So your answer would be B) a translation 10 units down followed by a translation 8 units to the right

Answer 2

B) a translation 10 units down followed by a translation 8 units to the right.

Explanation:

As in rotation, reflection and translation the transformed image is congruent to the original figure(i.e all the points undergo same change), so analyzing any one point will give the series of transformation undertaken.

Taking point A(-6, 4) into consideration.

Translating a point (x, y) k units down, it becomes (x, y-k).

So translated 10 units down point A, it becomes (-6, -6).

Translating a point (x, y) k units right, it becomes (x+k, y)

So translated 8 units right point (-6, -6), it becomes (2, -6)

This is the coordinates for A'.

Therefore, quadrilateral ABCD underwent a translation 10 units down followed by a translation 8 units to the right.