Question

find the value of a so that the points (1,4),(2,7),(3,a) are collinear​

Answer 1

Answer:

If points are collinear slope is constant.

∴ (4 - 7)/(1 - 2) = (a - 4)/(3 - 1)

⇒ 3 = (a - 4)/2

⇒ a = 10

∴ The value of a is 10.

Answer 2

Given

Points A(1,4) B (2,7) & C(3,a)

To Find

Value of a so that the points are collinear.

$\sf\huge\bold{\underline{\underline{{Solution}}}}$

To show that the three points are given then the slope of all three points must be equal to each other.

e.g.,Slope of AB must be equal to slope of BC

We will find slope of AB

A(1,4) & B(2,7)

Slope of AB= y₂ -y₁ / x₂-x₁

=>Slope of AB= 7-4/2-1

=>Slope of AB= 3

Now,slope of BC

B(2,7) C(3,a)

Slope of BC= y₂ -y₁ / x₂-x₁

=>Slope of BC= a-7/3-2

=>Slope of BC=a-7

Now,Slope of AB=slope of BC

=>3=a-7

=>a= 3+7

=>a=10

Check

Slope of AB = 3

Slope of BC= a-7=10-7=3

Slope of AB=slope of BC