Locate points in all four quadrants

By UK GCSE Mathematics · independent study · myAudience

Original myAudience mathematics teaching illustration; labels, relationships and lesson calculations independently checked. · Original project artwork; no exam-board figures or textbook illustrations reused.

Locate points in all four quadrants

A coordinate pair gives a horizontal position first and a vertical position second. For (−1, −1), move one unit left from the origin and one unit down. The origin is (0, 0); a point on an axis has one coordinate equal to zero and is not inside a quadrant.

The four quadrants are distinguished by signs: (+,+), (−,+), (−,−), (+,−), moving anticlockwise from the upper right. Read the scale before plotting. A square on paper need not represent one unit, and the two axes can use different numerical scales.

Coordinates connect pictures to calculations. A table of input x and output y becomes a collection of plotted points. Check a point against the rule that generated it rather than trusting its appearance on a grid.

Worked example: Plot the point (−2, 3).

Start at the origin.

Move two x-units left, then three y-units up.

Mark the intersection, using the actual axis scales.

Answer: The point lies in the upper-left quadrant.

Check your understanding: Which axis contains (0, −4)?

Answer: The y-axis.

Why: Its horizontal coordinate is zero.