Question

The perpendicular bisector of the straight line joining the points (3,2) and (5,6) meets the x-axis at A and the y-axis at B. prove that the distance AB is equal to 6√5.​

Answer 1

midpoint = ((3 + 5)/2, (2 + 6)/2) = (4, 4)

slope = (6 - 2)/(5 - 3) = 4/2 = 2

The perpendicular bisector will have slope -1/2 and will go through (4, 4).

4 = (-1/2)(4) + b

4 = -2 + b

b = 6

y = (-1/2)x + 6

y = 0--->x = 12, so A is at (12, 0).

x = 0--->y = 6, so B is at (0, 6).

AB = √(12² + 6²) = √180 = √36√5 = 6√5