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

Distance between two points A(x1, y1) and B(x2, y2) is given by

D = √(x2 - x1)2 + (y2 - y1)2

Let us assume that points (5, - 2), (6, 4), and (7, - 2) are representing the vertices A, B, and C of the given triangle respectively as shown in the figure.

AB = [(5- 6)2 + (-2- 4)2]1/2

=

=

BC = [(6- 7)2 + (4 + 2)2]1/2

=

=

CA = [(5- 7)2 + (-2+ 2)2]1/2

=

= 2

Therefore, AB = BC

As two sides are equal in length, therefore, ABC is an isosceles triangle

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