Math Problem Statement
The midpoint M of CD has coordinates (0.5, –3.5). Point D has coordinates (–13, –18). Find the coordinates of point C.
Write the coordinates as decimals or integers.
Solution
To find the coordinates of point C, we can use the midpoint formula. The midpoint of a line segment with endpoints and is given by the formula:
We are given the midpoint and the coordinates of point D . Let the coordinates of point C be . We can set up the equations for the midpoint:
Solving for the x-coordinate:
Multiply both sides by 2: Add 13 to both sides:
Solving for the y-coordinate:
Multiply both sides by 2: Add 18 to both sides:
Thus, the coordinates of point C are .
Let me know if you'd like further clarification or if you have any questions!
Here are 5 related questions to expand on this:
- How would the midpoint formula change if the midpoint had been given as a point in three-dimensional space?
- What would happen to the coordinates of point C if point D had different coordinates, say ?
- Can the midpoint of a line segment be used to find coordinates in a triangle, and if so, how?
- How can you use the midpoint formula to check if a set of points is symmetrically distributed?
- How would you use the distance formula to find the length of the line segment between points C and D?
Tip: Always check your calculations by substituting the values back into the midpoint formula to verify the result!
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Math Problem Analysis
Mathematical Concepts
Midpoint Formula
Coordinate Geometry
Algebra
Formulas
Midpoint formula: M = ((x1 + x2)/2, (y1 + y2)/2)
Theorems
Midpoint Theorem
Suitable Grade Level
Grades 7-9
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