Question

Prove that the points (3,0),(6,4) and (-1,3) are the verticles of a right angled isosceles triangle

Answer 1

Let the vertices of the triangle be
A(3,0) B(6,4) C(-1,3)

Distance formula = √(x₂-x₁)²+(y₂-y₁)²

Using distance formula;

AB
= √(3)²+(4)²
= 5 units

BC
= √(7)²+(1)²
= √50 units

AC
= √(4)²+(-3)²
= 5 units
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And :

5²+5² = (√50)²
(AB)²+(AC)² = (BC)²
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As two sides of triangle are equal in length
i.e AB=AC
and the sides of triangle are Pythagoras triplet, hence the given triangle is isosceles right angled triangle
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