Math Problem Statement
The midpoint M of PQ has coordinates (3.5, –4.5). Point Q has coordinates (–2, –6). Find the coordinates of point P.
Write the coordinates as decimals or integers.
Solution
To find the coordinates of point , we can use the midpoint formula. The midpoint of a segment with endpoints and is given by:
Given:
- Midpoint
- Point
We can set up the following equations based on the midpoint formula:
Step 1: Solve for
Multiply both sides of the first equation by 2:
Add 2 to both sides:
Step 2: Solve for
Multiply both sides of the second equation by 2:
Add 6 to both sides:
Final Answer:
The coordinates of point are .
Would you like more details or have any questions about the steps?
Here are five related questions:
- How would the midpoint change if point was moved further away from ?
- What is the distance between points and ?
- Can you find the slope of the line passing through points and ?
- How would you find the coordinates of a point that divides the segment in a different ratio?
- What are the coordinates of the midpoint if were at ?
Tip: Always verify your answers by substituting the coordinates back into the midpoint formula to check for consistency.
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Math Problem Analysis
Mathematical Concepts
Coordinate Geometry
Midpoint Formula
Formulas
Midpoint formula
Theorems
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Suitable Grade Level
Grades 7-9
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