Question

If the mid-point of the line joining (3, 4) and (k, 7) is (x, y) and 2 x + 2 y + 1 = 0. find the value of k.

Answer 1

Since (x,y) is the midpoint, using midpoint formula
$x = \frac{3 + k}{2} \: \: and \: \: y = \frac{4 + 7}{2} = \frac{11}{2} \\ given \: \: 2x + 2y + 1 = 0 \\ (3 + k) + 11 + 1 = 0 \\ k = - 15$