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If the points A (1, 2), O (0, 0) and C (a, b) are collinear, then
a. a = b
b.a = 2b
c. 2a = b
d. a = –b

Solution:

As the given points are collinear, it does not form a triangle

It means that the area of triangle is zero

We know that

Area of triangle with vertices (x₁, y₁), (x₂, y₂) and (x₃, y₃) is

\(\left | \frac{x_{1}(y_{2}-y_{3})+x_{2}(y_{3}-y_{1})+x_{3}(y_{1}-y_{2})}{2} \right |\)

The points given are

(x₁, y₁) = (1, 2)

(x₂, y₂) = (0, 0)

(x₃, y₃) = (a, b)

By substituting these values

\(\left | \frac{1(0-b)+0(a-1)+a(2-0)}{2} \right |=0\)

So we get

-b + 2a = 0

2a = b

Therefore, if the points are collinear, then 2a = b.

✦ Try This: If the points P (3, 4), O (0, 0) and Q (a, b) are collinear, then

☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 7

NCERT Exemplar Class 10 Maths Exercise 7.1 Problem 20

If the points A (1, 2), O (0, 0) and C (a, b) are collinear, then a. a = b, b. a = 2b, c. 2a = b, d. a = –b

Summary:

If the points A (1, 2), O (0, 0) and C (a, b) are collinear, then 2a = b

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