Question

What are the coordinates of the point on the directed line segment from left bracket, minus, 8, comma, 5, right bracket(−8,5) to left bracket, minus, 1, comma, minus, 2, right bracket(−1,−2) that partitions the segment into a ratio of 5 to 2?

Answer 1

The coordinates of the point that partitions the line segment into a ratio of 5 to 2 are (-3, 0).

To find the coordinates of the point that partitions the line segment into a ratio of 5 to 2, we first find the total change in the x-coordinate and y-coordinate. For the x-coordinate, we have (-1 - (-8)) = 7. For the y-coordinate, we have (-2 - 5) = -7.

Next, we multiply the change in x and y by the ratio of 5/7 to find the change in x and y for the point. So, the change in x is (7 * 5/7) = 5 and the change in y is (-7 * 5/7) = -5.

Finally, we add the change in x and y to the starting point (-8, 5) to find the coordinates of the point. So, the coordinates of the point are (-8 + 5, 5 - 5) = (-3, 0).

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