Question

Does the line 3x − 5y = 6 bisect the join of (5, −2) and (−1, 2)?

Answer 1

The given line will bisect the join of A(5, −2) and B(−1, 2), if the co-ordinates of the mid-point of AB satisfy the equation of the line.

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

`((5 - 1)/2, (-2 + 2)/2)`

= `(4/2, 0/2)`

= (2, 0)

Substituting x = 2 and y = 0 in the given equation, we have:

L.H.S. = 3x − 5y

= 3(2) − 5(0)

= 6 − 0

= 6 = R.H.S.

Hence, the line 3x − 5y = 6 bisect the join of (5, −2) and (−1, 2).