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in the figure below Point D is 2/3 of the way from E to F What are the coordinates of D if the coordinates of E and F are (2,−1) and (8,−4) respectively.

A. (5,−2.5)
B. (6,−3)
C. (4,−2)
D. (−2,0)

1 answer

To find the coordinates of point D, we need to find a point that is 2/3 of the way from E to F.

First, we find the differences in the x and y coordinates between E and F:
Δx = 8 - 2 = 6
Δy = -4 - (-1) = -3

To find the 2/3 point of these differences, we multiply them by 2/3:
2/3 * 6 = 4
2/3 * -3 = -2

Next, we add these differences to the coordinates of E (2, -1):
x-coordinate of D = 2 + 4 = 6
y-coordinate of D = -1 + (-2) = -3

Therefore, the coordinates of point D are (6, -3).

Answer: B. (6,−3)
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