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

By mid-point formula,

Mid-point of (5, -2) and (-1, 2) = $\dfrac{5 + (-1)}{2}, \dfrac{-2 + 2}{2}$

= $\dfrac{4}{2}, \dfrac{0}{2}$

= (2, 0).

Substituting x = 2 and y = 0 in L.H.S. of the equation 3x - 5y = 6.

L.H.S. = 3 × 2 - 5 × 0

= 6.

Since, L.H.S. = R.H.S.,

∴ (2, 0) lies on the line 3x - 5y = 6.

Hence, the line 3x – 5y = 6 bisects the join of (5, -2) and (-1, 2).