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Grade 6 · Maths · Lessons
All four corners
➕axes↗️quadrant 1↖️quadrant 2🪞mirror
All four corners.
The big ideaThe signs of a pair tell its corner. A mirror changes the signs.

How it works

The signs of a pair tell its corner: (+, +) is the top right, quadrant 1. (−, +) is the top left, quadrant 2. (−, −) is the bottom left, quadrant 3. (+, −) is the bottom right, quadrant 4.

A mirror changes the signs: across the x-axis flips the sign of y, and across the y-axis flips the sign of x.

Across both axes flips both.

Top• quadrant 2 (−, +)• quadrant 1 (+, +)Bottom• quadrant 3 (−, −)• quadrant 4 (+, −)
The four corners.

Example 1: Which corner?

  1. The point is (5, 1).
  2. Both numbers are positive.
  3. It is in quadrant 1, top right.

Example 2: Mirror over the x-axis

  1. A is at (−3, −2).
  2. Across the x-axis the y sign flips.
  3. The mirror point is (−3, 2).

Example 3: Mirror over both

  1. A is at (−10, 3).
  2. Both signs flip.
  3. The mirror point is (10, −3).

Words to know

quadrant
One of the four corners of the graph.
axis
A number line on a graph.

Watch out

Try it

  1. Which quadrant is (−2, 5) in?
  2. Which quadrant is (3, −4) in?
  3. Mirror (4, 6) across the x-axis.
  4. Mirror (4, 6) across the y-axis.
Answers: 1. quadrant 2 · 2. quadrant 4 · 3. (4, −6) · 4. (−4, 6)
For grown-upsDraw axes on the pavement with chalk and hop to points in every corner.
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