SOLUTION: triangle PQR, with P=(3,6), Q=(4,1), R=(14,3), find the measure of the largest angle of the triangle PQR.

Algebra ->  Triangles -> SOLUTION: triangle PQR, with P=(3,6), Q=(4,1), R=(14,3), find the measure of the largest angle of the triangle PQR.       Log On


   

Question 548540: triangle PQR, with P=(3,6), Q=(4,1), R=(14,3), find the measure of the largest angle of the triangle PQR.

Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
triangle PQR, with P=(3,6), Q=(4,1), R=(14,3), find the measure of the largest angle of the triangle PQR. 


The largest angle is at Q.  It looks like a right angle.
If it is, then the slopes of the lines PQ and QR will be
opposite signed reciprocals

Find the slope of PQ

m = %28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29

m = %281-6%29%2F%284-3%29

m = %28-5%29%2F1

m = -5

Find the slope of QR

m = %28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29

m = %283-1%29%2F%2814-4%29

m = 2%2F10

m = 1%2F5

-5 and 1%2F5 are opposite signed reciprocals, that is,

their product is -5·1%2F5 = -1.

So PQ and QR are perpendicular, so angle Q is 90°

Edwin