Question

Carmen performed two transformations on the blue figure. What transformations did she perform to get the red figure?

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

B) a translation of 5 units right and 1 unit down followed by a reflection across the x axis

C) a reflection across the x axis followed by a reflection across the y axis

D) a translation of 5 units right and 1 unit down followed by a rotation of 90 degrees clockwise about the origin

Answer 1

B) a translation of 5 units right and 1 unit down followed by a reflection across the x axis.

Explanation:

We know that when a transformation is performed in the given figure then each of the points of the figure also get transformed by the same rule.

Hence, we will check here the transformation by taking a point.

In the original figure the vertices of D are (-1,2) and that in the image the vertices of D' are (4,-1)

• Now, when a translation of 5 units is done to the right the rule of transformation is:

(x,y) → (x+5,y)

i.e.

Point D is transformed to:

(-1,2) → (-1+5,2)

i.e.

(-1,2) → (4,2)

• Also, the image is then shifted 1 units down i.e. the rule of transformation is:

(x,y) → (x,y-1)

i.e.

(4,2) → (4,2-1)

i.e. (4,2) → (4,1)

• Now, finally it is reflected across the x-axis i.e. the rule of transformation is:

(x,y) → (x,-y)

i.e.

(4,1) → (4,-1)

Hence, D(-1,2) → D'(4,-1)

Similarly other points of the figure are also transformed.

Answer 2

B) a translation of 5 units right and 1 unit down followed by a reflection across the x axis