☰ Year plan · Mathematics

The coordinate plane and reflections

Week 24 Β· The four quadrants, ordered pairs and reflections Β· 3 lessons
2

Points in all four quadrants: the signs of the coordinates

Discover Mathematics P6: Term 2, Unit 11, Lessons 1–3
GoalFind the quadrant of a point from the signs of its coordinates, and recognise points on the axes.
New words
sign Β· whether a number is positive (+) or negative (βˆ’)on an axis Β· a point with x = 0 or y = 0 lies on an axisanticlockwise Β· the direction opposite to the hands of a clock
Explanation

The signs of x and y tell us the quadrant. Quadrant I (top right): x positive, y positive (+, +). Quadrant II (top left): x negative, y positive (βˆ’, +). Quadrant III (bottom left): both negative (βˆ’, βˆ’). Quadrant IV (bottom right): x positive, y negative (+, βˆ’). A point with y = 0 lies on the x-axis, for example (4, 0). A point with x = 0 lies on the y-axis, for example (0, βˆ’3). A point on an axis is in NO quadrant. To find a quadrant, look at the sign of x first (left or right), then the sign of y (down or up).

QuadrantSign of xSign of yExample
I (top right)++(3, 2)
II (top left)βˆ’+(βˆ’3, 2)
III (bottom left)βˆ’βˆ’(βˆ’3, βˆ’2)
IV (bottom right)+βˆ’(3, βˆ’2)
Worked examples
In which quadrant is (βˆ’5, 6)? x is negative (left) and y is positive (up), so the point is in Quadrant II.
In which quadrant is (7, βˆ’1)? x is positive and y is negative, so the point is in Quadrant IV. And (βˆ’2, βˆ’8) has two negative signs, so it is in Quadrant III.
xyβˆ’5βˆ’4βˆ’3βˆ’2βˆ’112345βˆ’5βˆ’4βˆ’3βˆ’2βˆ’1123450EF
The points E(4, 0) and F(0, βˆ’3) are on the axes. E has y = 0, so it is on the x-axis. F has x = 0, so it is on the y-axis. Neither is in a quadrant.
Class activity

Quadrant game. Write eight ordered pairs on cards (two for each quadrant, using small numbers). Shuffle them. Pick a card and say its quadrant before you plot it. Plot it to check.

Practice
1
In which quadrant is (βˆ’4, βˆ’7)?
2
In which quadrant is (8, 3)?
3
Where is the point (0, 5)?
4
A point is in Quadrant IV. Which signs do its x and y have?
5
Write one point in each quadrant, using numbers from 1 to 9.