Question

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

Answer 1

Answer:

yes they are

Step-by-step explanation:

triangle with two sides of equal length and third of another length is called isosceles triangle

Here,

by using the formula [(x2-x1)^2 +(y2-y1)^2]^1/2

we can find the distance between these points

so, distance between:

(5,-2) & (7,-2)=2

(7,-2) & (6,4)= 37^1/2

(5,-2) & (6,4)=37^1/2

Therefore, given are the vertices of isosceles triangle.

Answer 2

Answer:

Step-by-step explanation:

We can check the same by application of 'distance formula' which is used to find the distance between two points whose coordinates are known.

If A(x₁, y₁) and B (x₂, y₂) represent 2 points in same plane, then by distance formula, the distance 'd' between these points is given by

d = √ (x₂ - x₁)² + (y₂ - y₁)²

Let the given points be written as:

A (5,-2)

B (6, 4)

C (7, -2)

AB = √(6 - 5)² + (4+2)² = √( 1 + 36) =  √37 units

BC = √(7 - 6)² + (-2-4)² = √(1 + 36) = √37 units

CA = √(7-5)² + (-2+2)² = √(4+0) = 2 units

As, AB = BC = √37 units; The given vertices indeed form an isosceles trianlge.