Partition the line segment by starting at the beginning of the line segment and moving forward a parts. Draw a point and verify that it is b parts from the end of the line segment. That's not so. Let's first take the easy case where P is at the origin and line segment is a horizontal one. The length of the line is 6 units and the point on the segment 1 3 of the way from P to Q would be 2 units away from P, 4 units away from Q and would be at ( 2, 0). Consider the case where the segment is not a horizontal or vertical line.
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