What are the coordinates of the point on the directed line segment from (-9, -1)(−9,−1) to (-9, -10)(−9,−10) that partitions the segment into a ratio of 2 to 1?

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The x coord of these points is the same (-9) so the line segment is vertical. Therefore the x coord of the required point will be -9. The length of the line is 9 units (between -1 and -10) so the line divides into 3 smaller segments each of length 3. So we take 2 segments together to make the longer of two segments to give us the ratio 2:1 that is, 2×3:1×3 or 6:3. If we start at y=-1 and go 6 units down towards y=-10 we get the y coord -1-6=-7. Put the coords together and we get the point (-9,-7).

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