Question

How to prove that by joining the points ( 2,1 ) , ( 3,4 ) , ( - 3,6 ) we get a right triangle? ​

Answer 1

SOLUTION

TO PROVE

The triangle joining the points ( 2,1 ) , ( 3,4 ) , ( - 3,6 ) is a right angled triangle

CONCEPT TO BE IMPLEMENTED

Two lines is said to be perpendicular if product of their slopes = - 1

EVALUATION

Let the given points are

A ( 2,1 ) , B ( 3,4 ) , C ( - 3,6 )

∴ Slope of the line AB

$\displaystyle \sf{m_1 = \frac{4 - 1}{3 - 2} = \frac{3}{1} = 3}$

∴ Slope of the line BC

$\displaystyle \sf{m_2 = \frac{6 - 4}{- 3 - 3} = \frac{2}{ - 6} = - \frac{1}{3} }$

$\displaystyle \sf{ \therefore \: m_1 \times m_2 = - 1}$

So the lines AB & BC are perpendicular

So ∠ ABC = 90°

So the triangle is a right angled triangle

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