Missing coordinate in triangle geometry

Question

Triangle abc has vertices with a (x,3) b(-3,-1) and c (-1-4) determine and state a value of x that would make triangle abc a right triangle

Answer 1

You can find the slope between the points b and c.  Once you have that slope, find the slope between points a and b. The slope between either of those combinations should be the negative reciprocal.

 

I will show you the process.

 

Step 1:

 

Find slope between points b and c.  These points when connected together form one leg of triangle (bc).

 

slope = (-4 - (-1)) / (-1 - (-3))

        = -3 / 2

 

 

Step 2:

 

Find the slope between points a and b.  The connection between these points form the second leg (ab).  This leg must be perpendicular to the first leg.  Because of this, the slope between the points will be the negative reciprocal.

 

Lets take the slope between points a and b.

 

(-1 - 3) / (-3 - x) = 2 / 3

 

 

Solve for x from this equation.