Partitioning Line Segments
This worksheet focuses on partitioning line segments in a given ratio, including finding coordinates on a number line and in the coordinate plane.
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Partitioning Line Segments
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Read each question carefully and follow the instructions to partition the line segments as required. Show all your work.
1. Points A and B are on a number line at coordinates -5 and 15, respectively. Find the coordinate of point P that partitions the segment AB in the ratio 2:3.
2. If a point P partitions a line segment AB into a ratio of 1:4, it means that the distance from A to P is of the total length of AB, and the distance from P to B is of the total length of AB.
3. Given points A(1, 2) and B(7, 10), find the coordinates of point P that partitions the segment AB in the ratio 1:3.
4. Point C is on segment DE. If DC = 8 and CE = 4, what is the ratio of DC to DE?
1:2
2:3
2:1
3:2
5. Explain how partitioning a line segment in a ratio of 1:1 relates to finding the midpoint of the segment. Then find the midpoint of a segment with endpoints (-2, 5) and (4, -1).
6. To partition a line segment AB in a ratio m:n, you can use the formula P = ( (n*A + m*B) / (m+n) ) for coordinates.
True
False