Let A= (0, 9) and B (0, 12). Points A’ and B’ are on the line y = x, line segments AA’ and BB’ intersect at C= (2, 8). What is the length of line segment A’B’?

coordinates of points A' and B' are equal since they lie on line of equation y=x

Slope of AC = Slope of CA'

8-9/2-0 = p-8/p-2

so, p = 6 ----- (i)

Slope of BC  = Slope of CB'

8-12/2-0  =  r-8/r-2

so, r  = 4 -----(ii)

Now,   (A'B')²  = (p-r)² + (p-r)²

          A'B' = 2.829 units