Question

The coordinates of the endpoints of EF are E(1,15) and F(15,8). Point G is on EF and divides it such that EG:FG is 5:2. What are the coordinates of G?

A) (7,12).
B) (10,10).
C) (12,10).
D) (8,13).

Answer 1

The coordinates of Point G, which divides the line segment EF in a 5:2 ratio where E is (1,15) and F is (15,8), are calculated using the section formula and are found to be (11, 10), which is not listed among the provided answer choices.

Step-by-step explanation:

The student is asking for the coordinates of Point G that divides the line segment EF into a 5:2 ratio, where E has coordinates (1,15) and F has coordinates (15,8).

To find the coordinates of G, we will use the section formula which is given by:

G(x, y) = ((mx2 + nx1) / (m + n), (my2 + ny1) / (m + n))

where E(x1, y1), F(x2, y2), m and n are the ratio in which G divides the line segment EF and G(x, y) are the coordinates we are looking to find.

Substituting the given values, we get:

G(x, y) = ((5*15 + 2*1) / (5 + 2), (5*8 + 2*15) / (5 + 2))

which simplifies to:

G(x, y) = (75 + 2) / 7, (40 + 30) / 7

G(x, y) = 77 / 7, 70 / 7

G(x, y) = (11, 10)

Therefore, none of the given options A) (7,12), B) (10,10), C) (12,10), or D) (8,13) are correct. The coordinates of Point G are actually (11, 10).