Question

Line segment EG is partitioned by point F in the ratio 1:3. Point E is at E (0, 4), and point F is at (1, 3). What are the coordinates of point G? (−1, 5) (2, 2) (3, 1) (4, 0)

Answer 1

(4,0)

Explanation:

Line segment EG is partitioned by point F in the ratio 1:3.

This means that:

`F - E = (1)/(4)(G - E)`

We use this equation to find both the x-coordinate and the y-coordinate of point G.

x-coordinate:

x-coordinate of E: 0

x-coordinate of F: 1

x-coordinate of G: x

Then

`F - E = (1)/(4)(G - E)`

`1 - 0 = (1)/(4)(x - 0)`

`1 = (x)/(4)`

`x = 4`

y-coordinate:

y-coordinate of E: 4

y-coordinate of F: 3

y-coordinate of G: y

Then

`F - E = (1)/(4)(G - E)`

`3 - 4 = (1)/(4)(y - 4)`

`-1 = (y-4)/(4)`

`y - 4 = -4`

`y = 0`

What are the coordinates of point G?

x = 4, y = 0, so (4,0).