Question

If points E(−20,15) and F(8,−20) are endpoints of EF, and EF is divided into two parts by point G in a 3:4 ratio, what are the two possible locations of G?

a) (-12, 0)
b) (-4, -8)
c) (0, -12)
d) (4, -16)

Answer 1

The two possible locations of point G, which divides the line segment EF in a 3:4 ratio, are (-12, 0) and (-4, -8).

Step-by-step explanation:

To find the two possible locations of point G, we need to divide the distance between points E and F into two parts in a 3:4 ratio. The total distance between E and F is the square root of [(8 - (-20))^2 + (-20 - 15)^2], which is equal to 49.

Dividing this distance into a 3:4 ratio gives us two possible locations for point G:

1. G1: Move 3/7 of the total distance from point E towards point F. Starting from point E, this gives us the coordinates (-20 + (3/7)(28), 15 + (3/7)(-35)), which simplifies to (-12, 0).
2. G2: Move 4/7 of the total distance from point E towards point F. Starting from point E, this gives us the coordinates (-20 + (4/7)(28), 15 + (4/7)(-35)), which simplifies to (-4, -8).