Without using the Pythagoras theorem, show ...

NCERT Class XI Mathematics - Straight Lines - Solutions

Question : 6 of 74

Marks: +1, -0

Without using the Pythagoras theorem, show that the points (4, 4), (3, 5) and (–1, –1) are the vertices of a right angled triangle.

Solution:

Let A(4, 4), B(3, 5) and C(–1, –1) be the vertices of ΔABC.

Let

m_1

and

m_2

be the slopes of AB and AC respectively.

Then,

m_1

= slope of AB =

\frac{5-4}{3-4}

= - 1

m_2

= slope of AC =

\frac{-1-4}{-1-4}

\frac{-5}{5}

= 1

∴

m_1m_2

= - 1

So, AB ⊥ AC and therefore ∠CAB = 90°.

Hence, the given points are the vertices of a right angled triangle.

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