Math Problem Statement
The midpoint of start overline, AB, end overline AB is M, left parenthesis, minus, 4, comma, 0, right parenthesisM(−4,0). If the coordinates of AA are left parenthesis, minus, 7, comma, 3, right parenthesis(−7,3), what are the coordinates of BB?
Solution
To find the coordinates of point , we use the formula for the midpoint between two points. The midpoint of a line segment connecting points and is given by:
We know:
- The coordinates of are ,
- The coordinates of are .
Let represent the unknown coordinates of point .
Using the midpoint formula:
Now, solve each equation:
For the -coordinate:
Multiply both sides by 2: Add 7 to both sides:
For the -coordinate:
Multiply both sides by 2: Subtract 3 from both sides:
Thus, the coordinates of are .
Would you like more details or have any questions? Here are 5 related questions to deepen your understanding:
- How do you derive the midpoint formula?
- What happens if one or both coordinates of are negative?
- Can you apply this method to 3-dimensional points?
- How can you verify your answer using the distance formula?
- What if the midpoint is given in terms of variables?
Tip: Always check your work by substituting back into the original equations to ensure consistency.
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Math Problem Analysis
Mathematical Concepts
Geometry
Coordinate Geometry
Formulas
Midpoint formula: M(x_m, y_m) = ((x_a + x_b)/2, (y_a + y_b)/2)
Theorems
-
Suitable Grade Level
Grades 8-10
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