Question

Find the coordinates of the intersection of the diagonals of parallelogram GHJK with vertices G(0,2). H(4,2), J(3,0), and K(-1,0).

The coordinates are?​

Answer 1

The coordinates of the intersection of the diagonals of parallelogram GHJK are (4, 2).

Step-by-step explanation:

To find the coordinates of the intersection of the diagonals of parallelogram GHJK, we can first find the equations of the diagonals using the given vertices. The equations of the diagonals are GH: y = 2 and JK: y = -x/4 + 2.

Next, we can solve these equations simultaneously to find the point of intersection. Substituting y = 2 into the equation of JK, we get 2 = -x/4 + 2. Solving for x, we find x = 4.

Finally, substituting x = 4 into the equation of GH, we get y = 2. Therefore, the coordinates of the intersection of the diagonals are (4, 2).