The coordinates of A are (-7,4) and the coordinates of G are (3,-10). How do you determine and state the coordinates of M if AG is partitioned into a ratio of 1:3?

Oct 18, 2017

Coordinates of G are $\left(- 4 \left(\frac{1}{2}\right) , - 6 \left(\frac{1}{2}\right)\right)$

A (-7, 4)
G (3, -10)
B midpoint of AG (-2, -3)
M midpoint of AB (-4(1/2), -6(1/2)
Now AM : MG is 1 : 3

Explanation:

A (-7, 4)
G (3, -10)
B midpoint of AG (-2, -3)
M midpoint of AB (-4(1/2), -6(1/2)
Now AM : MG is 1 : 3

Let Mid point of AG be B.
Coordinates of B are then given by
$x = \frac{3 + \left(- 7\right)}{2} = - 2 , y = \frac{\left(- 10\right) + 4}{2} = - 3$
$B \left(- 2 , - 3\right)$

G is now the midpoint of AB.
Coordinates of G are
$x = \frac{\left(- 2\right) + \left(- 7\right)}{2} = - 4 \left(\frac{1}{2}\right)$
$y = \frac{\left(- 10\right) + \left(- 3\right)}{2} = - 6 \left(\frac{1}{2}\right)$
Coordinates of G are $\left(- 4 \left(\frac{1}{2}\right) , - 6 \left(\frac{1}{2}\right)\right)$