Problem 22 · 2013 Math Kangaroo
Stretch
Geometry & Measurement
Fractions, Decimals & Percents
spatial-reasoning
The sides of rectangle ABCD are parallel to the coordinate axes. The rectangle lies below the x-axis and to the right of the y-axis, as shown. The coordinates of A, B, C, D are all whole numbers. For each point we work out (y-coordinate) ÷ (x-coordinate). Which point gives the smallest value?
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Answer: A — A
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Hint 1 of 2
All x-coordinates are positive and all y-coordinates are negative, so y/x is always negative.
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Hint 2 of 2
To make a negative value smallest, you want the most-negative y over the smallest x.
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Approach: compare y/x at the four corners
- Each point has x > 0 and y < 0, so every y/x is negative.
- The smallest (most negative) value comes from the largest |y| with the smallest x.
- Corner A is the lowest-left point: smallest x together with the most negative y.
- So point A gives the smallest value.
Mark:
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