Question

The perpendicular bisector of the line segment joining the points A(2,3) and B(5,6) cuts the y-axis at?​

Answer 1

Step-by-step explanation:

slope of line segment joining the points A(2, 3) and B(5, 6) , m = (6 - 3)/(5 - 2) = 1

slope of perpendicular on line joining the points A and B , m' = -1/m = -1

midpoint of AB = [(2 + 5)/2, (3 + 6)/2] = [7/2, 9/2]

now line passing through (7/2, 9/2) and perpendicular on line AB,

(y -9/2) = -1(x - 7/2)

at y - axis, x = 0

so, y - 9/2 = -1(0 - 7/2)

⇒y - 9/2 = 7/2

⇒y = 16/2 = 8