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

We know that the two sides of an isosceles triangle are equal.

To verify whether the given points are vertices of an isosceles triangle, we will determine the distance between all the points.

Let the points (5, – 2), (6, 4), and (7, – 2) are representing the vertices A, B, and C respectively. 

AB= √[(6 – 5)2 + (4+ 2)2]

= √[(-1)2 + (6)2]

=√37

BC= √[(7 – 6)2 + (-2 – 4)2]

= √[(-1)2 + (6)2]

=√37

CA= √[(7 – 5)2 + (-2 +2)2]

= √[(-2)2 + (0)2]

=2

Since the sides AB and BC are equal,

This indicates the given points are vertices of an isosceles triangle.

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