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Question

The points (5, - 2), (6, 4) and (7, - 2) are the vertices of an ________ triangle.

A
isosceles
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B
equilateral
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C
scalene
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Solution

The correct option is A isosceles
Let the points (5, - 2), (6, 4) and (7, - 2) represent the vertices A, B, and C of a triangle respectively.
Distance between the points is given by
(x1x2)2+(y1y2)2
BA=(56)2+(24)2
=(1)2+(6)2
=1+36=37
CB=(67)2+(4(2))2
=(1)2+(6)2
=1+36=37
CA=(57)2+(2(2))2
=(2)2+02=2
BA = CB
Two sides are equal in length.
So, ABC is an isosceles triangle.

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