Line segment eg is partitioned by point f in the ratio 1: 2. 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)

 The correct option is (C) (3, 1).

Step-by-step explanation:  Given that the line segment EG is partitioned by point F in the ratio 1 : 2. The point E is at E(0, 4) and the point F is at F(1, 3).

We are to find the co-ordinates of point G.

We know that

the co-ordinates of a point that divides the line segment joining the points (a, b) and (c, d) in the ratio m : n are given by

Let the co-ordinates of point G are (h, k).

Then, according to the given information, we have

and

Thus, the co-ordinates of point G are (3, 1).

Option (C) is CORRECT.

G = (3, 1 )

Step-by-step explanation:

Using the section formula, then equating a and y coordinates

= 1 ← x- coordinate of F

= 1 ( multiply both sides by 3 )

x = 3 ← x- coordinate of point G

and

= 3 ← y- coordinate of F

= 3 ( multiply both sides by 3 )

y + 8 = 9 ( subtract 8 from both sides )

y = 1 ← y- coordinate of G

Hence G = (3, 1 )

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step-by-step explanation: