الأسبوع 24 · قانون المساحة والمستوى الإحداثي · 3 دروس
2
Reading a coordinate plane
Discover Mathematics P5: Term 2, Unit 10, Lessons 5–8
GoalName the parts of a coordinate plane and read the ordered pair of a point.
New words
coordinate plane · a flat grid made by two number lines that cross at right anglesorigin · the point (0, 0) where the two axes meetordered pair · two numbers (x, y) that name a point; the order mattersaxis · one of the two number lines: the x-axis is horizontal, the y-axis is vertical
Explanation
A coordinate plane is made by two number lines. The horizontal one is the x-axis and the vertical one is the y-axis. They meet at the origin, which is the point (0, 0). In this book we use only the corner where all numbers are positive. A point is named by an ordered pair (x, y). The first number tells how far to go across along the x-axis, and the second tells how far to go up. A good rule is: walk along the corridor first, then climb the stairs. So the point (4, 2) is 4 units across and 2 units up, but (2, 4) is a different point: 2 across and 4 up. A point on the x-axis has y = 0, and a point on the y-axis has x = 0.
Worked examples
Point A is 4 units across and 2 units up, so A = (4, 2). Point B is 2 across and 4 up, so B = (2, 4). The pairs have the same numbers but the points are different places.
The school is at (5, 0) and the library is at (0, 5). The school is on the x-axis (y = 0) and the library is on the y-axis (x = 0).
Which point is farther to the right, (3, 7) or (6, 1)? Compare the first numbers (how far across): 6 is more than 3, so (6, 1) is farther to the right. (3, 7) is higher.
Class activity
Classroom treasure hunt. Draw a 6 by 6 grid on paper and number the lines 0 to 6 on both sides. One player hides a treasure at a crossing and the other guesses with ordered pairs: “(2, 5)?” The first player answers “hot” if the guess is one step away, and “cold” if not. Remember: across first, then up.
Practice
1
What are the coordinates of the origin?
(0, 0).
2
Write the ordered pair of the point that is 5 units across and 3 units up.
(5, 3).
3
A point is on the y-axis. What is its first coordinate?
0. For example (0, 4).
4
Which point is higher, (6, 2) or (1, 5)?
(1, 5). Compare the second numbers: 5 is more than 2.
5
Read the ordered pairs of points A, B and C on the plane.
