Coordinates and trigonometry · Ages 12–13
First steps in coordinates worksheet
Covers: Reading and plotting points, Quadrants and points on the axes, Distance along a horizontal or vertical line, Areas on the coordinate plane, Translation, Reflection, Rotation about the origin
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First steps in coordinates worksheet
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.
Part A: Working out and filling in (2 marks each)
1.The distance between A and B in the picture is units.
Answer:
2.A(−8, −7) and B(8, −7): A is units from the y-axis, B is units from it, so AB = units.
Fill in each blank
Answer:
3.Triangle ABC has corners A(−4, 2), B(3, 2) and C(−3, −4). Its area is square units.
Answer:
4.With a rectangle round triangle ABC: the rectangle's area = , the three corner right triangles together , so triangle ABC = square units.
Fill in each blank
Answer:
5.Reflected in the x-axis, (8, −3) goes to (, ).
Fill in each blank
Answer:
6.(2, 4) turned 90° clockwise about the origin goes to (, ).
Fill in each blank
Answer:
Part B: Choose, or true or false (2 marks each)
7.Which picture plots A(1, −4) and B(3, −2) correctly?
- A
- B
- C
- D
Choose the right picture
Answer:
8.Joining A(−1, −2), B(−5, 5) and C(−5, −3) in turn: which picture is right?
- A
- B
- C
- D
Choose the right picture
Answer:
9.Which point is in the 4th quadrant?
- A. (−8, −2)
- B. (−8, 2)
- C. (8, 2)
- D. (8, −2)
Choose the right answer
Answer:
10.Where is the point (3, 0)?
- A. At the origin
- B. On the x-axis
- C. Inside a quadrant
- D. On the y-axis
Choose the right answer
Answer:
11.Where does (2, −5) go when translated 1 unit to the left?
- A. (3, −5)
- B. (2, −6)
- C. (1, −6)
- D. (1, −5)
Choose the right answer
Answer:
12.A(1, −5) is translated to A′(3, −8). What is the translation?
- A. 2 units right, then 3 units down
- B. 2 units right, then 3 units up
- C. 2 units left, then 3 units down
- D. 3 units right, then 2 units down
Choose the right answer
Answer:
Part C: Word problems (4 marks each)
13.The point A(2m − 8, m − 2) is on the x-axis. m = , and A is (, ).
Fill in each blank
Working:
Answer:
14.With the pier at the origin and units of km, a fishing boat is at (3, 8) and a buoy at (3, −17). How far apart are they?
Working:
Answer:
15.Triangle ABC has area 8 square units, with A(−4, 2) and B(4, 2), and C above AB on the y-axis. What is C's y-coordinate?
Working:
Answer:
16.A square has corners (0, 0), (8, 0), (8, 8) and (0, 8). It is translated 5 units right. What area, in square units, do the square and its image share?
Working:
Answer:
17.A(−5, 6) reflected in the x-axis is B, and in the y-axis C. What is the area of triangle ABC, in square units?
Working:
Answer:
18.A(−3, 4) is turned 90° clockwise about the origin to B, and B reflected in the y-axis to C. B is (, ) and C is (, ).
Fill in each blank
Working:
Answer:
Show the answers and working
First steps in coordinates worksheet: Answers and working
Part A: Working out and filling in
1. 7
A(−4, 3) and B(3, 3) share one coordinate, so the distance is how far apart the other is: 7 units.
2. 8, 8, 16
The points are either side of the y-axis, so add the two parts: 8 + 8 = 16.
3. 21
AB is horizontal: base = 3 + 4 = 7; the height is C's distance up or down to AB, 6; area = 12 × 7 × 6 = 21.
4. 32, 22, 10
The rectangle round it: 4 × 8 = 32; the three corners 8 + 2 + 12 = 22; 32 − 22 = 10.
5. 8, 3
In the x-axis: x stays and y changes sign, giving (8, 3). The point and its image are both 3 from the x-axis.
6. 4, −2
90° clockwise: (x, y) goes to (y, −x). Swap them, then change the sign of the new y: (4, −2).
Part B: Choose, or true or false
7. D
A: from the origin go across to 1, then up or down to −4; B: across to 3, then to −2.
8. A
Plot one point at a time, across to x and then up or down to y, and join them in turn.
9. D. (8, −2)
Counting anticlockwise from the top right: first (+, +), second (−, +), third (−, −), fourth (+, −).
10. B. On the x-axis
A point with y = 0 is on the x-axis, one with x = 0 on the y-axis. (3, 0) has a 0, so it is on an axis, in no quadrant.
11. D. (1, −5)
1 unit left: take 1 from x, 2 − 1 = 1; y stays: (1, −5).
12. A. 2 units right, then 3 units down
x: 1 → 3, up by 2, so 2 right; y: −5 → −8, down by 3, so 3 down.
Part C: Word problems
Marking: 2 for the working, 1 for the answer, 1 for the sentence.
13. 2, −4, 0
On the x-axis, y = 0: m − 2 = 0, so m = 2; x = 2 × (2) − 8 = −4.
14. 25 km
Same x, so one vertical line, either side of the x-axis: 8 + 17 = 25 km.
15. 4
Base AB = 4 + 4 = 8; 12 × 8 × height = 8, so the height is 2. C is 2 above AB: 2 + 2 = 4.
16. 24
The image runs from x = 5 to 8 + 5; the shared part runs from x = 5 to x = 8: 3 wide and 8 tall, 3 × 8 = 24.
17. 60
AB is vertical, 2 × 6 = 12 long; AC is horizontal, 2 × 5 = 10; the right angle is at A, so the area is 12 × 12 × 10 = 60.
18. 4, 3, −4, 3
90° clockwise: (x, y) → (y, −x), B(4, 3); in the y-axis x changes sign: C(−4, 3).
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