A(1;4) B(-2;2) C(4;1) and M(x;y) are points on the Cartesian plane. Use analytical methods to determine the co-dinates of M so that ABCM, in this is a parallelogram

Question

Analytical geometry

Answer 1

M(x,y) = (7,3)

https://ibb.co/v35yQn9

Answer 2

The given points A, B and C are shown on the graph. The point A is 3 units to the right of B and 2 units higher. It follows then that if we go to point C 3 units to the right and 2 units higher we pinpoint M(7,3) making parallelogram ABCM. (We could have used the points B and C—C is 6 units to the right of B and 1 unit below. M is 6 units to the right of A and 1 unit below. This gives the same slope to BC and AM, just as AB and MC had the same slopes.)