# Check Whether (5, - 2), (6, 4) and (7, - 2) Are the Vertices of an Isosceles Triangle. - Mathematics

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

#### Solution

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

AB = sqrt((5-6)^2+(-2-4)^2) = sqrt((-1)^2+(-6)^2) = sqrt(1+36)  = sqrt37

BC = sqrt((6-7)^2+(4-(-2))^2)=sqrt((-1)^2+(6)^2) = sqrt(1+36)= sqrt37

CA = sqrt((5-7)^2+(-2-(-2))^2) = sqrt((-2)^2+0^2) = 2

Therefore AB = BC

As two sides are equal in length, therefore, ABCis an isosceles triangle.

Concept: Distance Formula
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#### APPEARS IN

NCERT Class 10 Maths
Chapter 7 Coordinate Geometry
Exercise 7.1 | Q 4 | Page 161