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What are the coordinates of the point on the directed line segment from (-6, -1) to (6,-9) that partitions the segment into a ratio of 3 to 1?

A. (-4, -7)
B. (0, -5)
C. (2, -7)
D. (4, -5)

1 Answer

3 votes

Final answer:

The partition point with a ratio 3 to 1 of the segment from (-6, -1) to (6, -9) is (3, -7), which can be found using the section formula. The calculated point is not among the options provided, suggesting an error in the question or options.

Step-by-step explanation:

The coordinates of the point that partitions the line segment from (-6, -1) to (6, -9) in a 3 to 1 ratio can be found using the section formula, which is an application of the weighted average.

For a line segment with endpoints (x1, y1) and (x2, y2) and a ratio of m:n, the coordinates (x, y) of the partitioning point are calculated using the formula:

x = (mx2 + nx1) / (m + n)

y = (my2 + ny1) / (m + n)

Plugging the given values and ratio 3:1 into the formula:

x = (3*6 + 1*(-6)) / (3 + 1)

y = (3*(-9) + 1*(-1)) / (3 + 1)

After solving, we get:

x = (18 - 6) / 4 = 12 / 4 = 3

y = (-27 -1) / 4 = -28 / 4 = -7

Therefore, the coordinates are (3, -7). However, this point is not among the options provided, which indicates there might be a mistake in the question or the choices given.

User Cozzamara
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