Math Problem Statement
Solution
To solve the problem of finding point on the line segment such that , we can follow these steps:
Step 1: Determine the coordinates of points and
- Point has coordinates .
- Point has coordinates .
Step 2: Apply the section formula
Since divides in the ratio , we use the section formula to find the coordinates of . The section formula for a point dividing a line segment internally in the ratio is given by:
Here:
- (coordinates of )
- (coordinates of )
Step 3: Calculate the coordinates of
So, the coordinates of point are .
Step 4: Plot the point
On the graph, locate the point at . This point should lie on the line segment .
Would you like further details, or have any questions on this solution?
Here are some related questions you might explore:
- How does the section formula apply when divides externally?
- What would be the coordinates of if the ratio was ?
- How can the midpoint formula be derived from the section formula?
- If point divided in a different ratio, how would you calculate it?
- How does the concept of weighted averages relate to the section formula?
Tip: Understanding the section formula can be particularly useful when solving problems involving line segments and ratios, especially in coordinate geometry.
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Math Problem Analysis
Mathematical Concepts
Coordinate Geometry
Ratios
Section Formula
Formulas
Section formula for internal division G(x, y) = ((mx2 + nx1) / (m+n), (my2 + ny1) / (m+n))
Theorems
Section Theorem
Suitable Grade Level
Grades 9-10
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