I have tried everything possible but I just can't seem to know the right answer. Can someone help me?

Question

Triangle END is reflected across the line y = x using the rule (x, y) → (y, x) to create triangle E′N′D′. If a line segment is drawn from point E to point E′, which statement would best describe the line segment drawn in relation to the line y = x?

A. Both are congruent to each other.

B. Both create diameters of concentric circles.

C. They are parallel.

D. They are perpendicular.

Answer 1

Let point E be (a, b), then point E' is (b, a)

The slope between the two points is (a - b) / (b - a) or a -1.

That is the negative reciprocal of the slope of y = x.

The line and segment are perpendicular.

Answer 2

We can sketch any triangle, assign points and then use the pattern above to figure out the solution.

You can see that the line y=x has a slope of 1.

next, take a point (4,-2) (You can pick any point) If you use the rule: (x, y) → (y, x) the new point after the translation is (-2,4). If we calculate the slope of the line that connects these 2 points,

m=(y2-y1)/(x2-x1) = [4-(-2)]/[-2-4] = 6/-6

m=-1

The 2 slopes. 1 and -1 are negative reciprocals. This means the lines are perpendicular to each other.

D. They are perpendicular.