Question

The coordinates of the vertices of parallelogram MATH are M(-7,5), A(6,5), T(4,-2), and H(-9,-2). What are the coordinate of G, the point of intersection of diagonals MT and ?

Answer 1

`G = (-1.5,1.5)`

Explanation:

Given

`M = (-7,5)`

`A = (6,5)`

`T = (4,-2)`

`H = (-9,-2)`

Required

Determine the coordinate of G

From the complete question, G is at the intersection of MT and AH.

So, G is calculated using midpoint formula

`G = (1)/(2)(x_1 + x_2, y_1 + y_2)`

For MT:

`M = (-7,5)`
`T = (4,-2)`

`G = (1)/(2)(-7 + 4, 5 -2)`

`G = (1)/(2)(-3, 3)`

Open bracket

`G = (-1.5,1.5)`

To show that
`G = (-1.5,1.5)`

We have:

`A = (6,5)`
`H = (-9,-2)`

`G = (1)/(2)(x_1 + x_2, y_1 + y_2)`

`G =(1)/(2)(6-9,5-2)`

`G = (1)/(2)(-3, 3)`

Open bracket

`G = (-1.5,1.5)`

Hence, the coordinates of G is:

`G = (-1.5,1.5)`