Question

A line segment has an end point of ( -4,-6) which reflection will produce an image with endpoints (-4, 6) and (-6,-4)

Answer 1

The given point is (-4, -6)

First reflected point is (-4, 6).
Note that the x coordinate is same and y coordinate has opposite sign. Above x-axis, y is positive and below x-axis y is negative. This shows that the reflection was across x-axis which resulted in the change of sign of y coordinate.

Second reflected point is (-6, -4)
Notice that in comparison to the original point, the location of x and y coordinate has been interchanged. This can only happen when the reflection is across the line y = x. The reflection of a graph across y = x also results in the inverse of that graph, with x values and y values interchanging their positions.

So,
1st Answer: Reflection across x-axis
2nd Answer: Reflection across the line y = x