AlgebraVery hardLine through the origin bisecting a rectangle
Algebra practice question
In the xy-plane, a rectangle has vertices (1, 2), (5, 2), (5, 6), and (1, 6). A line through the origin divides the rectangle into two regions of equal area. What is the slope of the line?
Answer: 4/3 or 1.333 or 1.33
A line through a rectangle's centre halves its area. The centre is (3, 4), so the slope is 4/3.
Common wrong answers
- If you answered 1
- 1 would pass through (3, 3), not the centre.
- If you answered 2
- 2 passes through (3, 6), a corner region.
- If you answered 3/4
- 3/4 inverts the slope.
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