First steps in coordinates · Ages 12–13
Quadrants and points on the axes
The signs give the quadrant; a 0 puts it on an axis.
How to do it
Method
The signs give the quadrant; a 0 puts it on an axis
(−4, 5): (−, +), the second quadrant
Another way
Plot and look
(−4, 5) lies up and left of the origin
In full
The axes cut the plane into four quadrants, counted anticlockwise from the top right: the first (+, +), the second (−, +), the third (−, −) and the fourth (+, −). The signs of x and y alone say which: (−4, 5) is in the second. A point on an axis is in no quadrant: on the x-axis its y-coordinate is 0, as (4, 0); on the y-axis its x-coordinate is 0, as (0, −3); the origin (0, 0) is on both. Or plot the point and see which side of the origin it lies.
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
Which point is in the 1st quadrant?
- A. (7, 9)
- B. (7, −9)
- C. (−7, −9)
- D. (−7, 9)
Choose the right answer
Show the answer and working
Answer: A. (7, 9)
Counting anticlockwise from the top right: first (+, +), second (−, +), third (−, −), fourth (+, −).
Example 2
Point P is on the x-axis, on the same vertical line as A(2, 1). P is (, ).
Fill in each blank
Show the answer and working
Answer: 2, 0
Points on one vertical line share x: x = 2. On the x-axis, y = 0.
Example 3
If (a, b) is in the 4th quadrant, then (−a, 3b) is in quadrant and (3b, a) in quadrant .
Fill in each blank
Show the answer and working
Answer: 3, 2
In the 4th quadrant the signs of a and b are known; −a has the opposite sign to a, and 3b the same as b. Sign by sign: quadrants 3 and 2.
Practice questions to try
Try these 5; the answers are at the end. For a whole worksheet, see VIP worksheets below.
1.The point (−2, −9) is in quadrant .
Answer:
2.Point P is 5 units from the y-axis and 3 units from the x-axis, in the 2nd quadrant. Which picture is right?
- A
- B
- C
- D
Choose the right picture
Answer:
3.Point P is on the x-axis, on the same vertical line as A(2, −3). P is (, ).
Fill in each blank
Answer:
4.The point P(4k − 24, −5) is on the y-axis. k =
Answer:
5.If (a, b) is in the 4th quadrant, then (−a, 4b) is in quadrant and (4b, a) in quadrant .
Fill in each blank
Answer:
All the answers
- 1. 3
- 2. B
- 3. 2, 0
- 4. 6
- 5. 3, 2
VIP practice notes and papers
Aimed at tests and exams: questions on this topic, new every time, to print or save as a PDF.
- Practice notes: The key point, worked examples step by step, then questions of the same kind to follow, hints fading
- Practice paper: Set out in parts like a school paper, marked, with answers and full working
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