What is the common point of the line AB and the first bisector if A(2,2) and B(1,3)?
We'll have to determine the intercepting point of the line AB and the line that represents the first bisectrix. For this reason, we'll have to solve the system formed from the equations of the line and the bisectrix.
The equation of the 1st bisectrix is y = x.
We'll have to determine the equation of the line AB.
We'll apply the formula;
(xB - xA)/(x - xA) = (yB - yA)/(y - yA)
(1 - 2)/(x - 2) = (3 - 2)/(y - 2)
-1/(x - 2) = 1/(y - 2)
-y + 2 = x - 2
We'll subtract 2 both sides:
-y = x - 4
y = -x + 4
The system that has to be solved is formed from the equations:
y = x (1)
y = -x + 4 (2)
We'll put (1) = (2):
x = -x + 4
We'll add x both sides:
2x = 4
We'll divide by 2:
x = 2
y = 2
We notice that the intercepting point is the point A(2 , 2).