Answer:
-2.5 , 0
Explanation:
-2.5 , 0
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To find the point F between E(-4,-2) and G(2,6) such that the ratio of EF to FG is 1:3, we can use the following steps:
1. Find the distance between E and G using the distance formula: √[(x2 - x1)^2 + (y2 - y1)^2]
- d(EG) = √[(6 - (-2))^2 + (2 - (-4))^2] = √(8^2 + 6^2) = √100 = 10
2. Since the ratio of EF to FG is 1:3, we can write:
- EF/FG = 1/3
- EF + FG = d(EG)
- Substituting EF = (1/4)d(EG), we get:
(1/4)d(EG) + 3(1/4)d(EG) = d(EG)
4(1/4)d(EG) = d(EG)
d(EF) = (1/4)d(EG) = (1/4)(10) = 2.5
3. Using the midpoint formula, we can find the coordinates of F:
- x-coordinate of F: (-4 + 2)/2 = -1
- y-coordinate of F: (-2 + 6)/2 = 2
Therefore, the point F between E(-4,-2) and G(2,6) such that the ratio of EF to FG is 1:3 is (-1, 2).
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