Question

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

Answer 1

If the line 3x - 5y = 6 bisect the join of (5, -2) and (-1, 2) then it passes through the midpoint of the join of (5, -2) and (-1, 2)

finding midpoint (x,y) from midpoint formula.


ie the midpoint is(2,0)

And substitute this in the line equation,

2(3)-5(0)=6 = RHS

it satisfies the line equation, hence line 3x - 5y = 6 bisect the join of (5, -2) and (-1, 2)