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To find a point that partitions a directed line segment in a given ratio, use the following steps: Step 2: Find the components of the directed line segment ...
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Example 1: The components of the vector from P to Q (the directed line segment PQ ) are 9 5, 6 4 = 4, 2. They tell you that a "route" from P to Q is 4 units right and 2 units up. Note that the components are used in the slope: 6 4 = 2 = 1 9 5 4 2
Step 3: Multiply the fraction found in step 1 by the components found in step 2. 2 4 = (^8) or 1.6 and 2 2 = 4 or 0. (^5 5 5 ) Step 4: Add the answer from step 3 to the first endpoint. This will give the coordinates of the partitioning point R. P (5, 4) (^) ⇒ R (5^ +^ 1.6,^4 +^ 0.8)^ ⇒ R (6.6,^ 4.8)
Example 2: Find the coordinates of point P along the directed line segment AB so that the ratio of AP to PB is 3 to 2. Example 3: Given the points A (1, 2) and B (7, 8), find the coordinates of point P on directed line segment AB that partitions AB in the ratio 1 / 3.
