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What are the coordinates of the point on the directed line segment from (- 2, -2) to (9, 9) that partitions the segment into a ratio of 5 to 6?

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Answer:

Step-by-step explanation:

The coordinates of the point that partitions the line segment from (-2, -2) to (9, 9) into a ratio of 5 to 6 is the point (5.5, 5.5).

To find the coordinates of this point, we need to use the formula for the midpoint of a line segment:

Midpoint = (x1 + x2)/2, (y1 + y2)/2

In this case, x1 = -2, x2 = 9, y1 = -2, y2 = 9.

Therefore, the midpoint = (-2 + 9)/2, (-2 + 9)/2

Substituting the values:

Midpoint = (7/2, 7/2)

Since the midpoint has to be in the ratio of 5 to 6, we divide each of the components of the midpoint by 11/6:

Midpoint = (7/2)/(11/6), (7/2)/(11/6)

Simplifying:

Midpoint = (15/22, 15/22)

Therefore, the coordinates of the point that partitions the line segment from (-2, -2) to (9, 9) into a ratio of 5 to 6 is the point (5.5, 5.5).

User Steve Coleman
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