Question

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

Answer 1

Vertices of a quadrilateral are A (7, 10), B(-2, 5) and C(3, -4) 

Using distance formula = \(\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\)

Since AB = BC 

Using Pythagoras theorem 

AC² = AB² + BC² 

\((\sqrt{212})^2\) = \((\sqrt{106})^2+ (\sqrt{106})^2\)

212 = 106 + 106 

212 = 212 

Therefore vertices are of right isosceles triangle.

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