Using the method of slopes show that the following points are collinear:

(i) A (4, 8), B (5, 12), C (9, 28)

(ii) A(16, – 18), B(3, – 6), C(– 10, 6)

Asked by Aaryan | 1 year ago |  63

##### Solution :-

(i) A (4, 8), B (5, 12), C (9, 28)

The slope of line AB =$$\dfrac{ 12 – 8 }{ 5 – 4}$$

$$\dfrac{4}{1}$$

The slope of line BC = $$\dfrac{ 28 – 12 }{ 9 – 5}$$

$$\dfrac{16}{4}$$

= 4

The slope of line CA =$$\dfrac{ 8 – 28}{4 – 9}$$

= $$\dfrac{ -20 }{ -5}$$

= 4

Here, AB = BC = CA

The Given points are collinear.

(ii) A(16, – 18), B(3, – 6), C(– 10, 6)

The slope of line AB = $$\dfrac{ 6 – (-18) }{ 3 – 16}$$

=$$\dfrac{12 }{ -13}$$

The slope of line BC =$$\dfrac{ 6 – (-6) }{ -10 – 3}$$

=$$\dfrac{12 }{ -13}$$

The slope of line CA = $$\dfrac{ 6 – (-18) }{ -10 – 16}$$

$$\dfrac{12 }{ -13}$$

= 4

Here, AB = BC = CA

The Given points are collinear.

Answered by Aaryan | 1 year ago

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