Curriculum placement
Geometry. This describes the skill, not a learner estimate.
Dividing a segment in a given ratio
Find a directed segment's internal or external proportional division point
Problem types
- Partition a segment in a ratio
- Point that divides a segment in a ratio
Builds on
- Coordinates in four quadrants
- Understanding ratios
- Proofs that use coordinates · Earlier idea
Coordinate proofs use midpoints, and a point dividing a segment in a given ratio extends the midpoint.
Leads to
- Motion described by a parameter · Extend the idea
The point a fraction t of the way from A to B is A + t(B - A), which is a parametric line.
- Vectors and their components · Extend the idea
A point that divides a segment in a ratio is the start point plus that fraction of the vector between the endpoints.
Related skills
- Using expected value to compare choices · Related idea
A point dividing a segment in ratio p to q is a weighted average of the endpoints, as an expected value weights each outcome by its probability.
- Distance and midpoints in the complex plane · Related idea
The midpoint of two complex numbers is their average, the same as the midpoint of a segment.
- Scale drawings of lengths and areas · Related idea
A point a fraction of the way along a segment is found by scaling the displacement, as a scale drawing scales distances.
- Distance in the coordinate plane · Shared foundations
- A graph as the solution set · Shared foundations
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