Problem 5 · 2024 Math Kangaroo
Medium
Spatial & Visual Reasoning
transformationsreflection
Julia has the strange habit of drawing the xy-plane with the positive directions of the coordinate axes pointing to the left and downwards. What does the graph of the equation \(y=x+1\) look like in Julia's coordinate system?
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Answer: D
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Hint 1 of 3
Reversing the direction of both axes is exactly a 180° rotation of the ordinary picture.
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Hint 2 of 3
A 180° turn keeps a line's slope, so the drawn line still rises to the right — only the labelled intercepts move.
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Hint 3 of 3
Rotate the standard graph of \(y=x+1\) half a turn and see which option's intercepts match.
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Approach: Julia's plane is the standard plane turned 180°
- Making both positive axes point the opposite way is the same as rotating the usual coordinate picture by \(180^\circ\).
- Under a \(180^\circ\) rotation the line \(y=x+1\) keeps its positive slope, so in Julia's drawing it still rises to the right.
- Its intercepts rotate to match exactly one of the pictures.
- That picture is option D.
Mark:
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