Math Problem Statement
Solution
The problem you've uploaded involves finding the coordinates of point Q on line segment MN, where the distance ratios are given as . The coordinates of point M are , and point N has coordinates .
To solve this, we can use the section formula, which finds the coordinates of a point dividing a line segment in a given ratio.
The section formula states that the coordinates of a point dividing a line segment joining and in the ratio are given by:
For your case:
- and ,
- The ratio , so and .
Now, applying the section formula:
For the -coordinate of Q:
For the -coordinate of Q:
Thus, the coordinates of point Q are .
Would you like more details on the section formula, or do you have any other questions related to this problem?
Further related questions:
- What would the coordinates of point Q be if the ratio was 3:2 instead of 2:3?
- How do you apply the section formula in 3-dimensional space?
- Can you find the midpoint of the line segment MN using the midpoint formula?
- What are the geometric interpretations of the ratios in the section formula?
- How do you apply the section formula when the line segment is vertical or horizontal?
Tip:
When solving problems involving line segments and ratios, always double-check the correct application of the section formula, as mixing up the coordinates or the ratio can lead to incorrect results!
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Math Problem Analysis
Mathematical Concepts
Coordinate Geometry
Section Formula
Ratio and Proportion
Formulas
Section formula: (x_Q, y_Q) = ((n*x1 + m*x2) / (m+n), (n*y1 + m*y2) / (m+n))
Theorems
Section Formula in Coordinate Geometry
Suitable Grade Level
Grades 8-10
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