Math Problem Statement
find the coordinates of point P along the directed line segment AB from A(-2,-8) to B(3,-3) so that the ratio of AP to PB is 3 to 2
Solution
To find the coordinates of point along the directed line segment from to such that the ratio of to is , you can use the section formula.
The section formula for a point dividing a line segment joining two points and in the ratio is given by:
Given:
- Ratio
Substituting the values into the section formula:
Calculating the coordinates of :
So, the coordinates of point are .
Would you like further details on this solution or have any questions?
Here are some related questions:
- How would the solution change if the ratio was instead of ?
- What are the coordinates of the midpoint of segment ?
- How do you find the distance between points and ?
- Can the section formula be used in three dimensions?
- What is the geometric interpretation of the section formula?
Tip: The section formula is a powerful tool to find points that divide a segment in any given ratio, and it can be extended to three dimensions as well.
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Math Problem Analysis
Mathematical Concepts
Coordinate Geometry
Section Formula
Ratio and Proportion
Formulas
Section formula for division of a line segment
Theorems
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Suitable Grade Level
Grades 9-12
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