Prove that the points (5, -2), (-4, 3) and (10, 7) are the vertices of – InterviewSolution

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1.	Prove that the points (5, -2), (-4, 3) and (10, 7) are the vertices of an isosceles right-angled triangle.
Answer» Let the points are `A(5,-2), B(-4, 3) and C(10, 7)`. `therefore" "AB^(2)=(-4-5)^(2)+(3+2)^(2)=(-9)^(2)+(5)^(2)= 81+ 25=106` `" "BC^(2)=(10+4)^(2)+(7-3)^(2)=(14)^(2)+(4)^(2)=196+16=212` `" "AC^(2)=(10-5)^(2)+(7+2)^(2) =(5)^(2)+(9)^(2)=25+81=106 ` Therefore, `" "AB=AC=sqrt(106)` `and " "AB^(2)+AC^(2)=BC^(2)` `thereforeDeltaABC` is an isosceles right-angled triangle.

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