Math Problem Statement
Solution
To solve the problem in the image, we need to find the coordinates of point such that the ratio of to is .
Step 1: Understand the Coordinates
Given:
- Ratio
Step 2: Apply the Section Formula
The section formula in coordinate geometry is used to find the coordinates of a point dividing a line segment in a given ratio. If a point divides the line segment joining and in the ratio , then the coordinates of are given by:
Here, and , , .
Step 3: Substitute the Values
Final Answer
The coordinates of point are .
Would you like more details or have any questions?
Related Questions:
- How is the section formula derived in coordinate geometry?
- What are other methods to find a point dividing a line segment?
- Can you explain the midpoint formula as a special case of the section formula?
- How would the coordinates change if the ratio was reversed to 3:4?
- How can you verify the answer using the distance formula?
Tip:
The section formula is a powerful tool not only for dividing line segments in a specific ratio but also for solving many geometric problems involving coordinate points.
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Math Problem Analysis
Mathematical Concepts
Coordinate Geometry
Ratios
Formulas
Section Formula: x = (mx2 + nx1) / (m+n), y = (my2 + ny1) / (m+n)
Theorems
Section Formula
Suitable Grade Level
Grades 9-12
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