NCERT Class XI Mathematics - Straight Lines - Solutions

Question : 6

Total: 74

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 m1 and m2 be the slopes of AB and AC respectively.
Then, m1 = slope of AB =

5−4

3−4

= - 1
m2 = slope of AC =

−1−4

= −

= 1
∴ m1m2 = - 1

So, AB ⊥ AC and therefore ∠CAB = 90°.
Hence, the given points are the vertices of a right angled triangle.

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