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

Given: Points $( 5,\ -2),\ ( 6,\ 4)$ and $( 7,\ -2)$ are given.

To do: To check whether the given points are the vertices of an isosceles triangle.

Solution:

Let $\vartriangle ABC$ be the isosceles triangle with the vertices $A( 5,\ -2),\ B( 6,\ 4)$ and $C( 7,\ -2)$.

On using the distance formula,

$AB=\sqrt{( 6-5)^2+( 4-( -2-))^2}=\sqrt{1+36}=\sqrt{37}$

$BC=\sqrt{( 7-6)^2+( -2-4)^2}=\sqrt{1+36}=\sqrt{37}$

$AC=\sqrt{( 7-2)^2+( -2-( -2))^2}=\sqrt{25}=5$

Since, $AB=BC=\sqrt{37}$

Hence, points $( 5,\ -2),\ ( 6,\ 4)$ and $( 7,\ -2)$ are the vertices of the isosceles triangle.

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Updated on: 10-Oct-2022

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