Question

If points (7,a), (-5,2) and (3,6) are collinear, find a.

(note: This is optional maths question )

Answer 1

The value of a is 8

Explanation:

If the three lines are collinear, they all lie on the same line

So let us have the equation of a line that passes through the known ends

the slope will be;

m = (6-2)/(3 + 5) = 4/8 = 1/2

The general form is;

y = mx + b

so, we have

y = 1/2x + b

To get b, we use any of the two known points

6 = 3/2 + b

b = 6-3/2

b = (12-3)/2 = 9/2

So the equation of the line is;

y = 1/2x + 9/2

Multiply through by 2

2y = x + 9

So for the point , to get a , we have that

2(a) = 7 + 9

2a = 16

a = 16/2

a = 8