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

Answer:

$G = (-1.5,1.5)$

Step-by-step 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

$G = \frac{1}{2}(x_1 + x_2, y_1 + y_2)$

For MT:

$M = (-7,5)$      $T = (4,-2)$

$G = \frac{1}{2}(-7 + 4, 5 -2)$

$G = \frac{1}{2}(-3, 3)$

Open bracket

$G = (-1.5,1.5)$

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

We have:

$A = (6,5)$       $H = (-9,-2)$

$G = \frac{1}{2}(x_1 + x_2, y_1 + y_2)$

$G =\frac{1}{2}(6-9,5-2)$

$G = \frac{1}{2}(-3, 3)$

Open bracket

$G = (-1.5,1.5)$

Hence, the coordinates of G is:

$G = (-1.5,1.5)$