SOLUTION: Can someone help me please?? thank you. Consider the points A(-2, 5), B(2, -3), C(8, 0), and P(4, 3). P is on the bisector of <ABC. Write an equation of the line in point-slope

Algebra ->  Number-Line -> SOLUTION: Can someone help me please?? thank you. Consider the points A(-2, 5), B(2, -3), C(8, 0), and P(4, 3). P is on the bisector of <ABC. Write an equation of the line in point-slope      Log On


   

Question 929360: Can someone help me please?? thank you.
Consider the points A(-2, 5), B(2, -3), C(8, 0), and P(4, 3). P is on the bisector of thanks !!
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
A(-2, 5), B(2, -3), C(8, 0), and P(4, 3).

Find the slope of AB and BC.
AB:
m=%28-3-5%29%2F%282-%28-2%29%29=-8%2F4=-2
BC:
m=%280-%28-3%29%29%2F%288-2%29=3%2F6=1%2F2
AB and BC are perpendicular since their slopes are negative reciprocals.
%28-2%29%281%2F2%29=-1
The angle between the two lines is then 90 so a bisector would split the angle into 2 45 degree segments.
The line BC makes an angle with the x-axis determined by the slope.
tan%28alpha%29=1%2F2
alpha=26.6 degrees
Adding 45 to this and then taking the tangent to find the slope,
m=tan%28alpha%2B45%29=tan%2871.6%29=3
Using the point slope form of a line with point B,
y-%28-3%29=3%28x-2%29
y%2B3=3x-6
highlight%28y=3x-9%29
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You could have also used point P and found the slope of BP.
m=%283-%28-3%29%29%2F%284-2%29=6%2F2=3
Continuing the same way as shown previously.