(8, -1) is reflected over the line y = x. What are the coordinates of the image?

Question

(8, -1) is reflected over the line y = x. What are the coordinates of the image?

Answer 1

Slope of line y = x is 1.

Slope of a perpendicular line is -1.

Equation of line with slope -1 and passing through (8, -1) is

y + 1 = -1(x - 8)

=> x + y = 7

Solving it with x = y gives the point of intersection as

(7/2, 7/2) which is the midpoint of (a, b) and (8, -1) where (a, b) are the coordinates of the image.

=> (a + 8)/2 = 7/2 and (b - 1)/2 = 7/2

=> a = -1 and b = 8

=> image is (-1, 8)

Thus, image in y = x can be obtained by swiching the x and y coordinates.

Answer 2

(-1, 8) - x and y coordinates switch  

Answer 3

The coordinates of the image are (-1,8)