Question

What are the coordinates of the point on the directed line segment from (-10, -3)(−10,−3) to (2, -3)(2,−3) that partitions the segment into a ratio of 5 to 3?

Answer 1

the coordinates of the point would be (-2.5,3)

Explanation:

We want to split the segment from (-10,-3) to (2,-3) into segments with a ratio of 5:3. Since the y-coordinate is -3 for both coordinates, the y-coordinate of the partitioning point will be -3. The ratio of 5:3 corresponds to 5/8 of the distance between the x-coordinates of the two points. So we would be moving 5/8 of the distance from -10 to 2 for the x-coordinate, so the x-coordinate would be -10 + 5/8 (12) = -2.5. So the coordinates of the point would be (-2.5,3)