Math Problem Statement
The midpoint of start overline, AB, end overline AB is M, left parenthesis, minus, 6, comma, 3, right parenthesisM(−6,3). If the coordinates of AA are left parenthesis, minus, 5, comma, 5, right parenthesis(−5,5), what are the coordinates of BB?
Solution
To find the coordinates of point , we can use the midpoint formula. The midpoint of a line segment between points and is given by:
We know:
Using the midpoint formula for each coordinate:
For the x-coordinate:
Multiply both sides by 2:
Solve for :
For the y-coordinate:
Multiply both sides by 2:
Solve for :
Final Answer:
The coordinates of are .
Would you like more details on this process?
Here are 5 related questions to explore:
- How do you find the midpoint of a line segment when both endpoints are given?
- What is the geometric significance of the midpoint in a coordinate plane?
- How can the midpoint formula be used to check if a line segment is bisected?
- If you change the coordinates of point , how does it affect the midpoint?
- How would you find the midpoint if one of the points is a variable, like ?
Tip: Always double-check your work by plugging your calculated point back into the midpoint formula to verify accuracy.
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Math Problem Analysis
Mathematical Concepts
Coordinate Geometry
Midpoint Formula
Formulas
Midpoint formula: M = ((x1 + x2)/2, (y1 + y2)/2)
Theorems
Midpoint Theorem
Suitable Grade Level
Grades 6-8
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