A triangle with vertices (4,0),(-1,-1),(3,5) is [AIEEE 2002]

Correct Answer is : isosceles and right angled

neither right angled nor isosceles

Correct Answer is : isosceles and right angled

Test Index

Straight Lines and Pair of Straight Lines Part 1

Section: Mathematics

Question : 97 of 100

Marks: +1, -0

(4,0),(-1,-1),(3,5)

Solution:

A B = \sqrt{(4+1)^2+(0+1)^2} = \sqrt{26}

B C = \sqrt{(3+1)^2+(5+1)^2} = \sqrt{52}

C A = \sqrt{(4-3)^2+(0-5)^2} = \sqrt{26}

In isosceles triangle side

A B = C A

For right angled triangle,

B C^2 = A B^2 + A C^2

So, here

B C = \sqrt{52}

B C^2 = 52

(\sqrt{26})^2 + (\sqrt{26})^2 = 52

So, the given triangle is right angled and also isosceles.

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