Question

Write an equation in slope-intercept form of the line that bisects the angle formed by BA and BC

Answer 1

Given:

Angled formed by ray BA and ray BC is 90 degrees.

To find:

The equation of line that bisects the angle formed by ray BA and ray BC.

Solution:

If a line bisects the angle formed by ray BA and ray BC, then it must be passes through point B and makes angles of 45 degrees with ray BA and ray BC.

It is possible if the line passes though point B(-1,3) and other point (-2,4).

Equation of line is

$y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)$

$y-3=\dfrac{4-3}{-2-(-1)}(x-(-1))$

$y-3=\dfrac{1}{-1}(x+1)$

$y-3=-x-1$

Add 3 on both sides.

$y=-x-1+3$

$y=-x+2$

Therefore, the required equation of line is $y=-x+2$.