Question

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?

Answer 1

Coordinates of G are `(-4(1/2), -6(1/2))`

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=(3+(-7))/2=-2, y =((-10)+4)/2=-3`
`B(-2, -3)`

G is now the midpoint of AB.
Coordinates of G are
`x=((-2)+(-7))/2=-4(1/2)`
`y=((-10)+(-3))/2=-6(1/2)`
Coordinates of G are `(-4(1/2), -6(1/2))`