Question

A circle with center C(4,-2) contains the point D(8, 1). What is the equation of the line perpendicular to the radius of the circle passing through point C?

Answer 1

if its algebra nation, its A, y= -4/3x + 10/3 :)

Answer 2

`y + 2 = -(4)/(3)(x-4)`

Explanation:

A perpendicular line is a line which has a negative reciprocal slope to the line. The slope can be found by writing the ratio between vertical and horizontal distance between the points.

`m = (y_2-y_1)/(x_2-x_1) = (1--2)/(8-4)=(3)/(4)`

This means the slope of the perpendicular line will be -4/3.

Substitute m = -4/3 and (4,-2) into the point slope form of a linear equation.

`y - -2 = -(4)/(3)(x - 4)\\y + 2 = -(4)/(3)(x-4)`