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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 =  √[(x₂ -  x₁)2 + (y₂ - y₁)2]

To find AB, that is distance between points A (5, - 2) and B (6, 4), let x₁ = 5, y₁ = -2, x₂ = 6, y₂ = 4

AB = √[( 6 - 5 )2 + (4 - (-2))2]

= √[(1)2 + (6)2]

= √1 + 36

= √37

To find BC, distance between Points B (6, 4) and C (7, - 2), let x₁ = 6, y₁ = 4, x₂ = 7, y₂ = - 2

BC = √ [( 7 - 6 )2 + (-2 - 4)2]

= √[(1)2 + (- 6)2]

= √1 + 36

= √37

To find AC, that is distance between Points A (5, - 2) and C (7, - 2), let x₁ = 5, y₁ = - 2, x₂ = 7, y₂ = - 2

AC = √ [( 7 - 5 )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.

☛ Check: NCERT Solutions for Class 10 Maths Chapter 7

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

Summary:

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

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