Question

A line segment with endpoints R(3, 5) and S(5, 5) is reflected across the line y = −x and translated 2 units down. Determine whether each choice is the image of an endpoint of the line segment. Select Yes or No for A-C.

A. R′(−5, −3)
a. Yes
b. No
B. R′(−5, −5)
a. Yes
b. No
C. S′(−5, −7)
a. Yes
b. No

Answer 1

Yes, R'(-5, -3) is the image of R(3, 5). Yes, R'(-5, -5) is the image of R(3, 5). Yes, S'(-5, -7) is the image of S(5, 5).

Step-by-step explanation:

To determine whether each choice is the image of an endpoint of the line segment, we need to apply the given transformations. First, we reflect the line segment across the line y = -x. This means that the x-coordinate and the y-coordinate of each point are flipped and negated. So, the image of R(3, 5) would be (-5, -3) and the image of S(5, 5) would be (-5, -5).

Next, we translate the line segment 2 units down. This means that we subtract 2 from the y-coordinate of each point. So, the new coordinates of the reflected points are R'(-5, -5) and S'(-5, -7).

1. For A, the image of R(3, 5) is R'(-5, -3). The given choice R'(-5, -3) matches the image, so the answer is Yes.
2. For B, the image of R(3, 5) is R'(-5, -5). The given choice R'(-5, -5) matches the image, so the answer is Yes.
3. For C, the image of S(5, 5) is S'(-5, -7). The given choice S'(-5, -7) matches the image, so the answer is Yes.