Question 1139696: triangle ABC is a right triangle. Sides AB and BC form the fight angle. The equation of the line is representing side AB is 4x+8y=16. If C is located at point (1,-3) What is the equation of the line representing side BC?
Answer by greenestamps(13198)   (Show Source):
You can put this solution on YOUR website!
A simplified form of the equation of the line containing AB is x+2y = 4.
Since there is a right angle at B, CB will be a line perpendicular to AB and containing point (1,-3).
One elementary way of solving the problem is to find the slope of AB, then find the slope of a line perpendicular to AB, then find the equation of the line with that slope containing (1,-3).
I leave it to you to solve the problem that way if you choose.
Here is a more advanced method for solving the problem.
Every line parallel to the line x+2y=4 has an equation of the form x+2y=c for some constant c (the coefficients of x and y remain the same);
Every line perpendicular to the line x+2y=4 has an equation of the form 2x-y=c for some constant c (the coefficients of x and y switch, and one of them changes sign).
So the line containing BC has an equation of the form 2x-y=c. Then, since that line contains the point (1,-3), we can easily determine the value of c:
So an equation of the line containing side BC is
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