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Coordinate Plane – Four Quadrants, Reflections and Distances

MathematicsVectors & Coordinate GeometryAges 13–14

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Drag two points A and B on the coordinate plane to read their coordinates, signs and quadrant; reflect A in the x- or y-axis and watch a coordinate change sign; find horizontal and vertical distances with absolute value. A 10-question game practises plotting, reading coordinates, quadrants, reflections and distances. The Polygons screen builds shapes from vertex coordinates and reads side lengths, perimeter and area.

Lesson: The coordinate plane: plotting points in all four quadrants

What it shows

The coordinate plane is split by the x-axis and y-axis into four quadrants, numbered I to IV anticlockwise from the top right. Each point is an ordered pair (x, y): x tells you how far to move right or left from the origin O, y how far up or down. Reflecting in the x-axis keeps x and changes the sign of y; reflecting in the y-axis does the opposite. Two points with the same y-coordinate are |x₂ − x₁| apart, which equals the sum of their distances from the y-axis when they lie on opposite sides of it.

How to use

On Explore, drag A and B (or tap the grid to move A) and read the quadrant and distance below. Choose Reflect A to show its images in the axes. On Game, pick a question type, then plot points or choose an answer; press Check and Next question, and New round to restart. On Polygons, choose a shape or tap to add vertices, drag them, and turn on an Image to reflect the whole shape.

Parameters you can change

  • Screen Explore, Game, Polygons
  • Grid size (from −n to n on each axis) 5–10
  • Point A: x-coordinate (Explore) -10–10
  • Point A: y-coordinate (Explore) -10–10
  • Point B: x-coordinate (Explore) -10–10
  • Point B: y-coordinate (Explore) -10–10
  • Reflect point A (Explore) No, In the x-axis, In the y-axis, In both axes
  • Shade and label the quadrants (Explore)
  • Question type (Game) Mixed, Plot points, Read coordinates, Quadrants, Reflections in the axes, Distances
  • Starting shape (Polygons) Rectangle, Right triangle, Trapezoid (trapezium), L-shape, Your own (empty grid)

Questions to explore

  1. What happens to the coordinates of a point when you reflect it in the x-axis, and in the y-axis?
  2. How far apart are (−3, 5) and (4, 5), and why can you add 3 and 4 to find it?
  3. Which vertex coordinates give a rectangle with perimeter 20 and area 24?

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