Week 24 Β· The four quadrants, ordered pairs and reflections Β· 3 lessons
1
The coordinate plane: axes, origin and ordered pairs
Discover Mathematics P6: Term 2, Unit 11, Lessons 1β3
GoalName the parts of the coordinate plane, and plot and read points using ordered pairs.
New words
ordered pair Β· two numbers (x, y) that give the place of a point; x always comes firstorigin Β· the point (0, 0) where the two axes crossquadrant Β· one of the four regions the axes divide the plane into
Explanation
The coordinate plane has two number lines that cross at right angles: the horizontal x-axis and the vertical y-axis. They cross at the origin, (0, 0). Numbers to the right of the origin and above it are positive; numbers to the left and below it are negative. The axes cut the plane into four quadrants, numbered anticlockwise starting at the top right. A point is named by an ordered pair (x, y). To plot it, start at the origin, move along the x-axis first (right if x is positive, left if negative), then up or down by y. Remember: x first, then y. The point (3, 2) and the point (2, 3) are different points.
Worked examples
Plot A(3, 2). Start at the origin, go 3 units right, then 2 units up. B(β2, 4): 2 units left, then 4 units up. A is in the first quadrant (top right) and B is in the second (top left).
Order matters. (3, 2) means 3 right and 2 up. (2, 3) means 2 right and 3 up. They are two different points, so we must never swap the numbers.
Read a point. C is 4 units left of the y-axis and 1 unit below the x-axis, so C = (β4, β1). D is 2 right and 3 down, so D = (2, β3).
Class activity
Treasure map. Draw a coordinate plane on squared paper. Hide a treasure at a point and write its ordered pair. Let a friend find it by moving along x first and then along y.
Practice
1
Write the coordinates of P, Q, R and S.
P(4, 3), Q(β3, 1), R(β2, β4), S(5, β2).
2
Describe how to plot the point (β5, 2) from the origin.
Go 5 units left, then 2 units up.
3
Which number comes first in an ordered pair, and which axis does it belong to?
The x-coordinate comes first. It belongs to the horizontal x-axis.
4
A point is 3 units right of the y-axis and 5 units below the x-axis. Write its ordered pair.
