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

**Solution:**

An isosceles triangle is a triangle that has two sides of equal length.

To check whether the given points are vertices of an isosceles triangle, we need to check the distance between any of the 2 points should be the same for two pairs of given points.

Let the points (5, - 2), (6, 4), and (7, - 2) represent the vertices A, B, and C of the given triangle

We know that the distance between the two points is given by the Distance Formula,

Distance Formula = √[(x_{2 - }x_{1})^{2} + (y_{2} - y_{1})^{2}]

To find AB, that is distance between Points A (5, - 2) and B (6, 4), let x_{1} = 5, y_{1} = -2, x_{2} = 6, y_{2} = 4

AB = √[( 5_{ - 6}_{ })^{2} + (-2 - 4)^{2}]

= √[(-1)^{2} + (-6)^{2}]

= √1 + 36

= √37

To find BC, distance between Points B (6, 4) and C (7, - 2), let x_{1} = 6, y_{1} = 4, x_{2} = 7, y_{2} = - 2

BC = √ [( 6_{ }- 7_{ })^{2} + (4 - (-2))^{2}]

= √[( -1_{ })^{2} + (6)^{2}]

= √1 + 36

= √37

To find AC, that is distance between Points A (5, - 2) and C (7, - 2), let x_{1} = 5, y_{1} = - 2, x_{2} = 7, y_{2} = - 2

AC = √ [( 5_{ }- 7_{ })^{2} + (-2 + 2)^{2}]

= √[( -2_{ })^{2} + (0)^{2}]

= 2

From the above values of AB, BC and AC we can conclude that AB = BC. As the two sides are equal in length, therefore, ABC is an isosceles triangle.

**Video Solution:**

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

### NCERT Class 10 Maths Solutions - Chapter 7 Exercise 7.1 Question 4:

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

The points (5, - 2), (6, 4), and (7, - 2) form an isosceles triangle