Question

Write an equation of the perpendicular bisector of the segment with endpoints G 9,8       and H 3,2      .

Answer 1

y = -x + 11

Explanation:

The equation of a straight line is is given by:

y = mx + b; where m is the slope and b is the y intercept

The equation of the line joining G(9, 8) and H(3, 2) is given as:

`y-y_1=(y_2-y_1)/(x_2-x_1)(x-x_1)\\\\y-8=(2-8)/(3-9)(x-9)\\\\y-8=x-9\\\\y=x-1`

The perpendicular bisector of the line joining G(9, 8) and H(3, 2) is perpendicular to the line joining G(9, 8) and H(3, 2) and passes through the midpoint of line joining G(9, 8) and H(3, 2).

Let (x, y) be the midpoint of the line joining G(9, 8) and H(3, 2). Hence:

x = (9 + 3)/2 = 6

y = (8 + 2)/2 = 5

The midpoint = (6, 5)

Two lines are perpendicular if the product of their slopes is -1.

The line joining G(9, 8) and H(3, 2) has a slope of 1, hence, the slope of the perpendicular bisector would be -1.

This means that the perpendicular bisector has a slope of -1 and passes through (6, 5). Using:

`y-y_1=m(x-x_1)\\\\y-5=-1(x-6)\\\\y-5=-x+6\\\\y=-x+11`

The equation of the perpendicular bisector is y = -x + 11