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. 
<pre>
{{{drawing(400,200,-2,16,-2,7,graph(400,200,-2,16,-2,7),

triangle(3,6,4,1,14,3), locate(3,6.6,"P(3,6)"), locate(4,1,"Q(4,1)"), 
locate(14,3,"R(14,3)")   )}}}

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 = {{{(y[2]-y[1])/(x[2]-x[1])}}}

m = {{{(1-6)/(4-3)}}}

m = {{{(-5)/1}}}

m = -5

Find the slope of QR

m = {{{(y[2]-y[1])/(x[2]-x[1])}}}

m = {{{(3-1)/(14-4)}}}

m = {{{2/10}}}

m = {{{1/5}}}

-5 and {{{1/5}}} are opposite signed reciprocals, that is,

their product is -5·{{{1/5}}} = -1.

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

Edwin</pre>