Distance, Midpoint, and Circles
A free College Algebra lesson from the “Relating Algebra and Geometry” unit, with a worked example and practice problems including step-by-step solutions.
Coordinate formulas connect algebra and geometry. Distance comes from the Pythagorean theorem, midpoint averages coordinates, and circle equations describe all points a fixed distance from a center.
What you'll learn
- Use distance and midpoint formulas
- Connect circle equations to geometry
- Interpret coordinate relationships
Worked example
Problem. Find the midpoint of (2, 9) and (8, 1).
- Average x-values: (2 + 8)/2 = 5.
- Average y-values: (9 + 1)/2 = 5.
- The midpoint is (5, 5).
Answer: (5, 5)
Lesson preview: this page shows 5 practice items. The interactive activity contains 28 practice items and 15 quiz items (multiple choice and typed response). Counts include repeated prompts and variants.
Practice problems
1. Find the midpoint of (0, 4) and (6, 10).
Choices: (3, 7) · (6, 14) · (3, 14) · (7, 3)
Show solution
- Average x and y values.
Answer: (3, 7)
2. Find the distance between (0, 0) and (3, 4).
Show solution
- Use a 3-4-5 triangle.
Answer: 5
3. For (x - 2)^2 + (y + 1)^2 = 25, what is the radius?
Show solution
- r^2 = 25.
Answer: 5
4. Find the midpoint of (2, 5) and (8, 1).
Choices: (5, 3) · (6, 4) · (10, 6) · (3, 5)
Show solution
- Average x-values and y-values.
Answer: (5, 3)
5. Find the distance between (-1, -2) and (2, 2).
Show solution
- The changes are 3 and 4.
Answer: 5
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