Question

Prove that the following points are the vertices of an isosceles triangle i)(4,1),(2,-5),(8,-3)

Answer 1

Given to prove :-

(4 ,1) , (2, -5) , (8, -3) are the vertices of Isoceless triangle .

Solution:-

To prove these are the vertices of Isoceless triangle then, For an Isoceless triangle two sides are equal .So, let's find distances between these points.

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Distance formula :- If the points are (x₁ , y₁) and (x₂ , y₂) then distance between those points is √(x₁-x₂)² +(y₁-y₂)²

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Let, A=(4,1) B=(2,-5), C=(8,-3)

A = (4, 1) = (x₁ , y₁)

B = (2, -5) = (x₂ , y₂)

So,

AB = √(x₁-x₂)² +(y₁-y₂)²

AB = √(4-2)² +[1-(-5)]²

AB = √(2)² +(1+5)²

AB= √4+36

AB= √40

B=(2, -5) = (x₁ , y₁)

C= (8, -3) = (x₂ , y₂)

BC = √(x₁-x₂)² +(y₁-y₂)²

BC = √(2-8)² +[-5-(-3)]²

BC = √(-6)² + (-5+3)²

BC = √(-6)² +(-2)²

BC= √36+4

BC = √40

A= (4, -1) = (x₁ , y₁)

C = (8, -3) = (x₂ , y₂)

AC = √(x₁-x₂)² +(y₁-y₂)²

AC = √(4-8)² +[-1-(-3)]²

AC = √(-4)² +(-1+3)²

AC = √(-4)² +(2)²

AC = √16+4

AC = √20

So,

From these distances we can say that

AB = BC = √40

Hence , given vertices are the vertices of Isoceless triangle

Hence proved !