Question

Prove that the abc is right triangle .the points a,b,c in a coordinate plane have the coordinates a(-1,1) , b(2,-1) and c(6,5).

Answer 1

Side AB=√13. [By using distance formula
BC=√52. distance=√{(x2-x1)²+(y2-y1)²}]
AC=√65
We can observe that,

(AB²)+(BC)²=(AC)²
(√13)²+(√52)²=(√65)²
13+52=65
65=65
Therefore triangle ABC obeys Pythagoras theorem so it is a right triangle.
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