Question

Write an equation in slop _intercept form of the line that bisects the angle formed by BA and BC

Answer 1

y = -x + 2

Explanation:

Angle between these lines = 90°

Angle between BC and the angle bisector BD = 45°

Since, m(∠DBE) = 90° + 45° = 135°

Therefore, slope of the angle bisector BD = tan(90° + 45°)

= -tan(45)°

= -1

Let the equation of the angle bisector which passes through (x', y') and slope = m,

y - y' = m(x - x')

Where m = slope of the line = (-1)

Since, the angle bisector passes through a point B(-1, 3),

Equation of BD will be,

y - 3 = (-1)(x + 1)

y - 3 = -x - 1

y = -x - 1 + 3

y = -x + 2