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)](https://tex.z-dn.net/?f=y-y_1%3D%5Cdfrac%7By_2-y_1%7D%7Bx_2-x_1%7D%28x-x_1%29)
![y-3=\dfrac{4-3}{-2-(-1)}(x-(-1))](https://tex.z-dn.net/?f=y-3%3D%5Cdfrac%7B4-3%7D%7B-2-%28-1%29%7D%28x-%28-1%29%29)
![y-3=\dfrac{1}{-1}(x+1)](https://tex.z-dn.net/?f=y-3%3D%5Cdfrac%7B1%7D%7B-1%7D%28x%2B1%29)
![y-3=-x-1](https://tex.z-dn.net/?f=y-3%3D-x-1)
Add 3 on both sides.
![y=-x-1+3](https://tex.z-dn.net/?f=y%3D-x-1%2B3)
![y=-x+2](https://tex.z-dn.net/?f=y%3D-x%2B2)
Therefore, the required equation of line is
.
The answer is
2. 2a+12
Show work
2a+7+2a+7+4+4= 4a+22
A+2+a+2+3+3 = 2a+10
(4a+22)-(2a+10) = 2a+12