Question

The line y = 3x – 2 bisects the join of (a, 3) and (2, −5), find the value of a.

Answer 1

The given line bisects the join of A(a, 3) and B(2, −5), so the co-ordinates of the mid-point of AB will satisfy the equation of the line.

The co-ordinates of the mid-point of AB are 

`((a + 2)/2, (3 - 5)/2)`

= `((a + 2)/2, (-2)/2)`

= `((a + 2)/2, -1)`

Substituting `x = (a + 2)/2 ` and y = –1 in the given equation, we have:

y = 3x – 2

`-1 = 3 xx (a + 2)/2 - 2`

`3 xx (a + 2)/2 = 1`

`a + 2 = 2/3`

`a = 2/3 - 2`

= `(2 - 6)/3`

= `(-4)/3`