Question

If the three points (3, – 1), (a, 3) and (1, – 3) are collinear, find the value of a

Answer 1

The vertices are A(3, – 1), B(a, 3) and C(1, – 3)

Slope of a line = `(y_2 - y_1)/(x_2 - x_1)`

Slope of AB = `(3 + 1)/("a" - 3) = 4/("a" - 3)`

Slope of BC =  `(3 + 3)/("a" - 1) = 6/("a" - 1)`

Since the three points are collinear.

Slope of AB = Slope BC

`4/("a" - 3) = 6/("a" - 1)`

6(a – 3) = 4(a – 1)

6a – 18 = 4a – 4

6a – 4a = – 4 + 18

2a = 14 

⇒ a = `14/2` = 7

The value of a = 7