Q15 of 49 Page 1

Prove that the points (7, 10), (-2, 5) and (3, -4) are the vertices of an isosceles right triangle.

Let A(7, 10), B(-2, 5) and C(3, -4) be the vertices of a triangle

Length of side AB is given by-




= √(81+25)


= √106 units


[using distance formula, the distance between points (x1,y1) and (x2,y2) is equal to units.]


Length of side BC is given by-




=√(25+81)


=√106 units


Length of side AC is given by-




=√(16+196)


=√212 units


∴ Δ ABC is an isosceles Δ.


Also,


AB2+BC2 = AC2 [By converse of Pythagoras’ theorem]


Thus, Points A, B, C are the vertices of an isosceles right triangle.


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Fig.4