SOLUTION: Show that the triangle formed by the points (-2,5), (1,3) and (5,9) is right angled

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Question 1045501: Show that the triangle formed by the points (-2,5), (1,3) and (5,9) is right angled
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

the triangle formed by the points A=(-2,5), B=(1,3) and C=(5,9)
we need to find sides length using distance formula
AB
(-2,5), (1,3)
d=sqrt%28%28x%5B1%5D-x%5B2%5D%29%5E2%2B%28y%5B1%5D-y%5B2%5D%29%5E2%29
d=sqrt%28%28-2-1%29%5E2%2B%285-3%29%5E2%29
d=sqrt%28%28-3%29%5E2%2B%282%29%5E2%29
d=sqrt%289%2B4%29
d=sqrt%2813%29
->AB=sqrt%2813%29
AC
(-2,5),(5,9)
d=sqrt%28%28x%5B1%5D-x%5B2%5D%29%5E2%2B%28y%5B1%5D-y%5B2%5D%29%5E2%29
d=sqrt%28%28-2-5%29%5E2%2B%285-9%29%5E2%29
d=sqrt%28%28-7%29%5E2%2B%284%29%5E2%29
d=sqrt%2849%2B16%29
d=sqrt%2865%29
->AC=sqrt%2865%29
BC
(1,3,(5,9)
d=sqrt%28%28x%5B1%5D-x%5B2%5D%29%5E2%2B%28y%5B1%5D-y%5B2%5D%29%5E2%29
d=sqrt%28%281-5%29%5E2%2B%283-9%29%5E2%29
d=sqrt%28%28-4%29%5E2%2B%28-6%29%5E2%29
d=sqrt%2816%2B36%29
d=sqrt%2852%29
->BC=sqrt%2852%29
so,
->AB=sqrt%2813%29
->AC=sqrt%2865%29->hypotenuse
->BC=sqrt%2852%29
if %28AC%29%5E2=%28AB%29%5E2%2B%28BC%29%5E2 the triangle formed by the points is right angled
%28sqrt%2865%29%29%5E2=%28sqrt%2813%29%29%5E2%2B%28sqrt%2852%29%29%5E2
65=13%2B52
65=65 which is true
so, the triangle formed by the points is right angled