Question 1139696
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A simplified form of the equation of the line containing AB is x+2y = 4.<br>
Since there is a right angle at B, CB will be a line perpendicular to AB and containing point (1,-3).<br>
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).<br>
I leave it to you to solve the problem that way if you choose.<br>
Here is a more advanced method for solving the problem.<br>
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);<br>
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).<br>
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:<br>
{{{2x-y = 2(1)-(-3) = 2+3 = 5 = c}}}<br>
So an equation of the line containing side BC is<br>
{{{2x-y = 5}}}