NavGanitMateby NavGreen Compute, AustraliaBased on Australian Curriculum: Mathematics v9.0
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Coordinate transformations

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A person starts at point A located at (37, 57) in the Cartesian plane. They walk 37 units west and 57 units south to reach point B.

Then, they reflect point B over the line y = x to obtain point C. What is the x-coordinate of point C?

Provide the exact value as a single number.

Concept illustrations

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Coordinates on a plane. Illustration: the point (2, 2) lies on y = x. Read x across, then y up.-2-2-1-111223344xy
Illustration: the point (2, 2) lies on y = x. Read x across, then y up.
Moving a parabola up three units. The solid parabola is y = x² + 3; the dashed parabola is y = x². Every output increases by 3, moving the vertex from (0,0) to (0,3).xy(0,3)y = x² + 3
The solid parabola is y = x² + 3; the dashed parabola is y = x². Every output increases by 3, moving the vertex from (0,0) to (0,3).

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Explanation

Worked solution and answer (click to reveal)

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Worked solution

  1. Point A is given at coordinates (37, 57) in the Cartesian plane.
  2. The person walks 37 units west, which means subtracting 37 from the x-coordinate.
  3. New x-coordinate after moving west: 37 - 37 = 0.
  4. The person walks 57 units south, which means subtracting 57 from the y-coordinate.
  5. New y-coordinate after moving south: 57 - 57 = 0.
  6. Point B is now at (0, 0).
  7. Point B is reflected over the line y = x to obtain point C.
  8. Reflection over y = x swaps the x and y coordinates of a point.
  9. Applying the reflection: (0, 0) becomes (0, 0).
  10. The x-coordinate of point C is therefore 0.
  11. Verification: Reflecting (0, 0) over y = x results in (0, 0), so the x-coordinate is unchanged.
  12. The x-coordinate of point C is exactly 0.

Reference answer: 0

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