Coordinates and trigonometry · Ages 12–13

Quadrants and points on the axes worksheet

Part of: First steps in coordinates

In the print window, choose “Save as PDF” to download it. The answers print on the last page.

Coordinates and trigonometry · Ages 12–13

Numsprite
numsprite.com

Name:Date:Score:／48

Write each answer in the space. For word problems, show your working and write a sentence answer.

1.The point (6, 9) is in quadrant .
Answer:
2.The point (−5, 2) is in quadrant .
Answer:
3.Point P is on the x-axis, on the same vertical line as A(2, −5). P is (, ).
Fill in each blank
Answer:
4.Point P is on the x-axis, on the same vertical line as A(4, 5). P is (, ).
Fill in each blank
Answer:
5.The point P(4k + 4, 1) is on the y-axis. k =
Answer:
6.If (a, b) is in the 3rd quadrant, then (−a, 5b) is in quadrant and (5b, a) in quadrant .
Fill in each blank
Answer:
7.The point P(3k − 3, 1) is on the y-axis. k =
Answer:

8.Which point is in the 3rd quadrant?
- A. (3, 2)
- B. (3, −2)
- C. (−3, −2)
- D. (−3, 2)
Choose the right answer
Answer:
9.The point (−6, −9) is in the 3rd quadrant.
True or false?
Answer:
10.The point (−7, −7) is in the 3rd quadrant.
True or false?
Answer:
11.Point P is 2 units from the y-axis and 6 units from the x-axis, in the 1st quadrant. Which picture is right?
- A
- B
- C
- D
Choose the right picture
Answer:
12.Where is the point (0, −9)?
- A. On the y-axis
- B. Inside a quadrant
- C. On the x-axis
- D. At the origin
Choose the right answer
Answer:

13.The point A(2m − 2, m − 2) is on the x-axis. m = , and A is (, ).
Fill in each blank
Working:
Answer:
14.The point (4 − k, 8) is in the second quadrant, and k is a whole number. What is the smallest k can be?
Working:
Answer:
15.How many points with whole-number coordinates lie in the 1st quadrant with −6 ≤ x ≤ 6 and −6 ≤ y ≤ 6?
Working:
Answer:
16.With the square at the origin, the x-axis east, the y-axis north and units of km, the museum lies south-east of the square, 3 km away east–west and 9 km north–south. The museum is at (, ).
Fill in each blank
Working:
Answer:
17.With a lighthouse at the origin, the x-axis is the east–west shipping lane. Which of these four boats is exactly on the lane?
- A. (−2, 1)
- B. (−6, −2)
- C. (1, −6)
- D. (1, 0)
Choose the right answer
Working:
Answer:
18.With the square at the origin, the x-axis east and the y-axis north, the museum lies south-west of the square, 2 km away east–west and 6 km north–south. Which quadrant is it in?
- A. The first
- B. The fourth
- C. The third
- D. The second
Choose the right answer
Working:
Answer:

Show the answers and working

Quadrants and points on the axes worksheet: Answers and working

1. 1
Look at the signs of 6 and 9: (+, +) is the first quadrant, (−, +) the second, (−, −) the third, (+, −) the fourth. So quadrant 1.
2. 2
Look at the signs of −5 and 2: (+, +) is the first quadrant, (−, +) the second, (−, −) the third, (+, −) the fourth. So quadrant 2.
3. 2, 0
Points on one vertical line share x: x = 2. On the x-axis, y = 0.
4. 4, 0
Points on one vertical line share x: x = 4. On the x-axis, y = 0.
5. −1
A point on the y-axis has x-coordinate 0: 4k + 4 = 0, so k = −1.
6. 4, 3
In the 3rd quadrant the signs of a and b are known; −a has the opposite sign to a, and 5b the same as b. Sign by sign: quadrants 4 and 3.
7. 1
A point on the y-axis has x-coordinate 0: 3k − 3 = 0, so k = 1.

8. C. (−3, −2)
Counting anticlockwise from the top right: first (+, +), second (−, +), third (−, −), fourth (+, −).
9. True
The signs of −6 and −9 decide it: the point is in the 3rd quadrant.
10. True
The signs of −7 and −7 decide it: the point is in the 3rd quadrant.
11. B
The first quadrant is top right, the second top left, the third bottom left, the fourth bottom right: anticlockwise from the top right.
12. A. On the y-axis
A point with y = 0 is on the x-axis, one with x = 0 on the y-axis. (0, −9) has a 0, so it is on an axis, in no quadrant.

Marking: 2 for the working, 1 for the answer, 1 for the sentence.

13. 2, 2, 0
On the x-axis, y = 0: m − 2 = 0, so m = 2; x = 2 × (2) − 2 = 2.
14. 5
In the second quadrant x is negative: 4 − k < 0, so k > 4. The smallest whole number is 5. At k = 4, x is 0 and the point is on the y-axis, in no quadrant.
15. 36
In the 1st quadrant neither x nor y may be 0: 6 choices for x and 6 for y, 6 × 6 = 36. Points on the axes don't count.
16. 3, −9
south-east: the 3 km east–west gives x and the 9 km north–south gives y; west and south are negative, so (3, −9).
17. D. (1, 0)
A point on the x-axis has y = 0: (1, 0) is on the lane, in no quadrant.
18. C. The third
East is positive x, west negative; north positive y, south negative. south-west puts it in the 3rd quadrant. The distances don't change the quadrant.

Numsprite · numsprite.com/en/worksheets/first-steps-in-coordinates/quadrants-and-points-on-the-axes