Given triangle ABC with vertices A(3,-1), B(2,2), and C(5,1). a)Find the slope of the angle bisector of angle ABC b)Prove that the bisector of angle ABC is the perpendicular bisector of AC

Answer 1

If you plot the triangle at the given points (ordered pairs) for A, B and C you'll have an isoceles triangle tilted up to the left. Why is it isoceles? Because sides AB and BC are equal. You can measure them or use the Pythagorean Theorem to figure it out. They're both length sqrt10. Given an isoceles triangle, the angle bisector will be perpendicular to its base. You can look up the proof on the web.

The bisector intersects the x-axis at (4,0). The slope of the bisector is rise/run = (4 - 2)/(0 - 2) = 2/-2 = -1. You can also see that on the plotted triangle. The equation of the bisector is y = -x + 4. When x = 0, y = 4 (the y-intercept). When y = 0, x = 4.