Question

figure n is transformed to figure n in 3 steps.
step 1: horizontal translation right 11 units
step 2: ________
step 3: reflection across the x - axis
which transformation is needed in step 2 to map figure n onto figure n?
a. vertical translation up 2 units
b. horizontal translation left 2 units
c. vertical translation down 2 units
d. horizontal translation right 2 units

Explanation:

Step1: Analyze Step 1 and Step 3

First, Step 1 is a horizontal translation right 11 units. Step 3 is a reflection across the x - axis. Let's consider the vertical position of the figures.

Step2: Compare vertical positions

Looking at the original figure N and the final figure N', after Step 1 (horizontal translation) and before Step 3 (reflection), we need to adjust the vertical position. The original figure N (before Step 2) and the intermediate figure (after Step 2) should have a vertical translation. By observing the y - coordinates of corresponding points, we can see that to get from the position after Step 1 to the position before Step 3 (so that Step 3 reflection gives N'), we need to translate the figure up by 2 units. Because when we reflect across the x - axis, the vertical position will be mirrored. So Step 2 should be a vertical translation up 2 units.

Answer:

A. vertical translation up 2 units