Math Problem Statement
The midpoint of start overline, AB, end overline AB is M, left parenthesis, minus, 1, comma, minus, 5, right parenthesisM(−1,−5). If the coordinates of AA are left parenthesis, 2, comma, minus, 4, right parenthesis(2,−4), what are the coordinates of BB?
Solution
To find the coordinates of point , given that is the midpoint of and the coordinates of , we can use the midpoint formula. The midpoint formula is given by:
Here, is the midpoint, are the coordinates of point , and are the coordinates of point .
We can set up the following equations based on the midpoint formula:
Now, solve for and .
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For the x-coordinate: Multiply both sides by 2: Subtract 2 from both sides:
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For the y-coordinate: Multiply both sides by 2: Add 4 to both sides:
Therefore, the coordinates of point are .
Would you like more details or have any questions?
Here are five related questions you might find interesting:
- How do you find the distance between two points?
- What is the formula for finding the slope of a line segment between two points?
- How can you determine if three points are collinear?
- What is the equation of the line passing through points and ?
- How do you find the area of a triangle given the coordinates of its vertices?
Tip: When using the midpoint formula, remember that the midpoint divides the line segment into two equal parts, so it's a great tool to find an unknown endpoint if the other endpoint and the midpoint are known.
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Math Problem Analysis
Mathematical Concepts
Coordinate Geometry
Midpoint Formula
Formulas
Midpoint formula: M = ((x1 + x2) / 2, (y1 + y2) / 2)
Theorems
The midpoint theorem
Suitable Grade Level
Grades 8-10
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