I need help with add math Coordinate Geometry

[Ahmed Iqbal123]

Three points have coordinates A(6,6), B(-3,3) and C(9,k). The foot of the perpendicular from A to BC is the midpoint of BC. Calculate the possible values of k.

 

[Varun_bzl]

Three points have coordinates A(6,6), B(-3,3) and C(9,k). The foot of the perpendicular from A to BC is the midpoint of BC. Calculate the possible values of k.

Let the foot of the perpendicular be P. The coordinates of P will be P(3,(3+k)/2) since it is the midpoint of BC.
Find the gradient of BC and AP in terms of k. Since AP and BC are perpendicular, it implies that :
gradient AP x gradient BC = -1
Hence, solve the quadratic equation.