Question

Question #1b20a

Answer 1

Equationn of perpendicular bisector is

`color(green)(7y - 3x = 4)`

Explanation:

Given : Points A(-2,8), B (4,-6)

To find the equation of perpendicular bisector thru P

Mid Point P will have coordinates

`P_x = (A_x + B_x)/ 2 = (-2 + 4) / 2 = 1`

`P_y = (A_y + B_y)/ 2 = (-6 + 8 / 2 = 1`

`P (1,1)`

Slope of AB

`m_(AB) = (y_b - y_a) / (x_b - x_a) = (-6-8) / (4 - (-2) = -14/6= -7/3`

Slope of perpendicular line to AB is

`m_P = -1 / (-7/3) = -3/-7 = 3/7`

Equation of perpendicular bisector through point P is

`y - y_P = (3/7) * (x - x_P)`

`y - 1 = (3/7) * (x - 1)`

`7y - 7 = 3x -3`

`color(green)(7y - 3x = 4)`