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The coordinate plane and reflections

الأسبوع 24 · الأرباع الأربعة والأزواج المرتبة والانعكاس · 3 دروس
1

The coordinate plane: axes, origin and ordered pairs

Discover Mathematics P6: Term 2, Unit 11, Lessons 1–3
GoalName the parts of the coordinate plane, and plot and read points using ordered pairs.
New words
ordered pair · two numbers (x, y) that give the place of a point; x always comes firstorigin · the point (0, 0) where the two axes crossquadrant · 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.

xy−5−4−3−2−112345−5−4−3−2−1123450ABCD
Worked examples
xy−5−4−3−2−112345−5−4−3−2−1123450AB
Plot A(3, 2). Start at the origin, go 3 units right, then 2 units up. B(−2, 4): 2 units left, then 4 units up. A is in the first quadrant (top right) and B is in the second (top left).
xy−5−4−3−2−112345−5−4−3−2−1123450PQ
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 = (−4, −1). D is 2 right and 3 down, so D = (2, −3).
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.
xy−5−4−3−2−112345−5−4−3−2−1123450PQRS
2
Describe how to plot the point (−5, 2) from the origin.
3
Which number comes first in an ordered pair, and which axis does it belong to?
4
A point is 3 units right of the y-axis and 5 units below the x-axis. Write its ordered pair.
5
What are the coordinates of the origin?