Find the distance from the origin to the midpoint of the line segment joining the points (2, 5) and (8, –3).
Answer
√26
The correct answer is √26 — Distance is √26 units.
Step-by-step solution
- Find the midpoint: ((x₁+x₂)/2, (y₁+y₂)/2).
- Compute x-coordinate: (2+8)/2 = 5.
- Compute y-coordinate: (5+(-3))/2 = 1.
- Midpoint is (5, 1).
- Use distance formula to origin: √((x-0)² + (y-0)²).
- Compute (5)² = 25.
- Compute (1)² = 1.
- Sum: 25 + 1 = 26.
- Take square root: √26.
- Distance is √26 units.
Common mistake: Forgetting to average the coordinates or misapplying the distance formula
Concept tested: Midpoint and distance to origin
Published · How this solution was prepared and checked
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