Question 884328
Well if your asking if that triangle is isosceles then you need to determine if all three sides are the same length, since for a triangle to be isosceles it needs to have all 3 sides the same length.  Which means finding the distance between P and Q, P and R, and Q and R.  <br>

To find the distance between two points we use the distance formula which is {{{d=sqrt((x2-x1)^2+(y2-y1)^2)}}}.  <br>

Now lets try finding the distance between P and Q.  P(2,-2) and Q(-4,5) from above and now we plug and chug: <br>

{{{d=sqrt((x2-x1)^2+(y2-y1)^2)}}}
={{{d=sqrt((-4-2)^2+(-5-(-2))^2)}}}
={{{d=sqrt((-6)^2+(-3)^2)}}}
={{{d=sqrt(36+9)}}}
={{{d=sqrt(45)}}}
={{{d=3sqrt(5)}}}<br>

Now lets try finding the distance between P and R.  P(2,-2) and R(8,9) so we plug and chug again. <b>

{{{d=sqrt((x2-x1)^2+(y2-y1)^2)}}}
={{{d=sqrt((8-2)^2+(9+2)^2)}}}
={{{d=sqrt((6)^2+(11)^2)}}}
={{{d=sqrt(36+121)}}}
={{{d=sqrt(157)}}}<br>

Since {{{sqrt(157)}}} is not the same as {{{3sqrt(5)}}} then the triangle is not isosceles.