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

Answer:

(4,0)

Step-by-step explanation:

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

This means that:

$F - E = \frac{1}{4}(G - E)$

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

$F - E = \frac{1}{4}(G - E)$

$1 - 0 = \frac{1}{4}(x - 0)$

$1 = \frac{x}{4}$

$x = 4$

y-coordinate:

y-coordinate of E: 4

y-coordinate of F: 3

y-coordinate of G: y

Then

$F - E = \frac{1}{4}(G - E)$

$3 - 4 = \frac{1}{4}(y - 4)$

$-1 = \frac{y-4}{4}$

$y - 4 = -4$

$y = 0$

What are the coordinates of point G?

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