AlgebraHardSlope of a line through the origin and a midpoint
Algebra practice question
In the xy-plane, the midpoint of the line segment from (1, 2) to (5, 8) lies on the line y = mx, where m is a constant. What is the value of m?
Answer: 5/3
The midpoint is ((1 + 5)/2, (2 + 8)/2) = (3, 5). Since it lies on y = mx: 5 = 3m, so m = 5/3.
Common wrong answers
- If you answered 2
- 2 comes from using the first endpoint (1, 2) instead of the midpoint.
- If you answered 3/5
- 3/5 is x over y, the reciprocal.
- If you answered 3/2
- 3/2 is the slope of the segment itself, (8 − 2)/(5 − 1).
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