Question

A line segment with endpoints R(3,5) and 5(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

The images of endpoints R(3,5) and S(5,5) after reflection across the line y=-x and translation 2 units down are R'(-5,-5) and S'(-5,-7), respectively. Point A (R'(5,-3)) is not the image of R, and point B (R'(-5,5)) does not match the transformations. However, point C (S'(-5, -7)) is the correct image of S.

Step-by-step explanation:

The question involves finding the images of endpoints of a line segment after reflection across the line y=-x and translation 2 units down. To reflect a point across the line y=-x, we switch its x and y coordinates and change their signs. Then, we translate the point 2 units down by subtracting 2 from the y-coordinate. Let's find the images of the endpoints R(3,5) and S(5,5).

• Reflecting R(3,5) gives R'(-5,-3), and translating it 2 units down gives R'(-5,-5), so R'(5,-3) is not the image. The answer is: a) No.
• Reflecting S(5,5) gives S'(-5,-5), and translating it 2 units down gives S'(-5,-7). So, S'(-5, -7) is the image. The answer is: a) Yes.

To summarize, the images after the transformation are R'(-5,-5) and S'(-5,-7). The choices given must be evaluated against these points.

1. For point A (R'(5,-3)) the answer is: b) No.
2. For point B (R'(-5,5)), since it does not match the y-coordinate of R', the answer is: b) No.
3. For point C (S'(-5, -7)), since it matches the image of S after transformation, the answer is: a) Yes.