Question

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

2,2

Step-by-step explanation:

I don't really know how to explain it, but if you plot E and F on a coordinate plane it would make more sense.

*Note that the ratio 1:1 is not the same as the fraction 1/1, rather, 1:1 = 1/2 so point F is like a midpoint of segment EG

Answer 2

The coordinates of point G is (2,2)

The coordinate points are given as:

• $E = (0,4)$

• $F = (1,3)$

The ratio is given as:

$m : n = 1 : 1$

Given that the ratio is 1 : 1, it means that, point F is at the midpoint of line segment EG

So, we have:

$F =0.5 \times (x_1 + x_2, y_1 + y_2)$

This gives

$(1,3) =0.5 \times (0 + x, 4+ y)$

$(1,3) =0.5 \times (x, 4+ y)$

Multiply both sides by 2

$(2,6) =(x, 4+ y)$

By comparison, we have:

$x = 2$

$4 + y = 6$

$y =2$

Hence, the coordinates of point G is (2,2)

Read more about line partitions at:

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