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Check whether the points (5, -2), (6, 4) and (7, -2) are the vertices of an isosceles triangle.

Coordinate Geometry

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Answer

Let points be A(5, -2), B(6, 4) and C(7, -2).

Check whether the points (5, -2), (6, 4) and (7, -2) are the vertices of an isosceles triangle. Coordinate Geometry, ML Aggarwal Understanding Mathematics Solutions ICSE Class 9.

By distance formula,

d = (x2−x1)2+(y2−y1)2\sqrt{(x2 - x1)^2 + (y2 - y1)^2}

AB=(6−5)2+[4−(−2)]2=12+62=1+36=37.BC=(7−6)2+[−2−4]2=12+(−6)2=37.AB = \sqrt{(6 - 5)^2 + [4 - (-2)]^2} \\[1em] = \sqrt{1^2 + 6^2} \\[1em] = \sqrt{1 + 36} \\[1em] = \sqrt{37}. \\[1em] BC = \sqrt{(7 - 6)^2 + [-2 - 4]^2} \\[1em] = \sqrt{1^2 + (-6)^2} \\[1em] = \sqrt{37}.

Since, AB = BC.

Hence, proved that (5, -2), (6, 4) and (7, -2) are the vertices of an isosceles triangle.

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