Question

A line segment with endpoints (7,5) and (10, 1) is reflected across the line y = -x. Which pair of coordinates represents the endpoints of the given segment after the reflection?

A (-7, 5) and (-10, 1)
B (-5, -7) and (-1, -10)
C(5, 7) and (1, 10)
D (7,-5) and (10,-1)​

Answer 1

After reflecting the line segment with endpoints (7,5) and (10,1) across the line y = -x, the transformed coordinates become (-5,-7) and (-1,-10), which corresponds to Option B.

Step-by-step explanation:

When a line segment is reflected across the line y = -x, you effectively switch the x and y coordinates and then change their signs; this is because reflecting over the line y = -x is the same as rotating the point 90 degrees clockwise around the origin and then reflecting it over the x-axis. The line segment with endpoints (7,5) and (10,1) will then have its endpoints transformed into (-5,-7) and (-1,-10) after the reflection. Therefore, the correct pair of coordinates after the reflection is Option B: (-5, -7) and (-1, -10).

Answer 2

D. (7,-5) and (10,-1)

Step-by-step explanation:

Because 7 and 10 are on the Y and -5 and -1 is on the X