(7, −9) turned 90° clockwise about the origin goes to (□, □). Fill in each blank

−9, −7. 90° clockwise: (x, y) goes to (y, −x). Swap them, then change the sign of the new y: (−9, −7).

Where does (−5, 3) go when turned 90° clockwise about the origin? A. (3, −5) B. (3, 5) C. (−3, −5) D. (5, −3) Choose the right answer

B. (3, 5). 90° clockwise: (x, y) → (y, −x), that is (3, 5). Check: it moves on one quadrant, clockwise.

(−4, 7) turned 270° anticlockwise about the origin goes to (□, □). Fill in each blank

7, 4. 270° anticlockwise is 90° clockwise: (x, y) → (y, −x), giving (7, 4). Or turn 90° anticlockwise three times.

First steps in coordinates · Ages 12–13

Rotation about the origin

180°: both signs change; 90°: swap, then change one sign.

How to do it

Method

180°: both signs change; 90°: swap, then change one sign

(4, 1): 90° anticlockwise (−1, 4); clockwise (1, −4)

Another way

Turn the right triangle

4 across, 1 up turns to 4 up, 1 left

In full

About the origin: through 180°, (x, y) goes to (−x, −y), both coordinates changing sign. 90° anticlockwise, (x, y) goes to (−y, x); 90° clockwise, to (y, −x): swap x and y, then change the sign of one of them. 270° anticlockwise is 90° clockwise. Without the rules: draw the right triangle from the origin, x across and y up, turn it through 90°, and see where its corner lands. Check: a quarter turn takes the point to the next quadrant (anticlockwise: first, second, third, fourth), the same distance from the origin.

Worked examples

Have a go first, then open each one for the answer and the working.

Example 1
(7, −9) turned 90° clockwise about the origin goes to (, ).
Fill in each blank
Show the answer and working
Answer: −9, −7
90° clockwise: (x, y) goes to (y, −x). Swap them, then change the sign of the new y: (−9, −7).
Example 2
Where does (−5, 3) go when turned 90° clockwise about the origin?
- A. (3, −5)
- B. (3, 5)
- C. (−3, −5)
- D. (5, −3)
Choose the right answer
Show the answer and working
Answer: B. (3, 5)
90° clockwise: (x, y) → (y, −x), that is (3, 5). Check: it moves on one quadrant, clockwise.
Example 3
(−4, 7) turned 270° anticlockwise about the origin goes to (, ).
Fill in each blank
Show the answer and working
Answer: 7, 4
270° anticlockwise is 90° clockwise: (x, y) → (y, −x), giving (7, 4). Or turn 90° anticlockwise three times.

Practice questions to try

Try these 5; the answers are at the end. For a whole worksheet, see VIP worksheets below.

1.(9, −5) turned 180° about the origin goes to (, ).
Fill in each blank
Answer:
2.Triangle ABC is turned 90° anticlockwise about the origin, to A′B′C′. Which picture is right?
- A
- B
- C
- D
Choose the right picture
Answer:
3.Where does (−2, 5) go when turned 90° clockwise about the origin?
- A. (5, −2)
- B. (5, 2)
- C. (2, −5)
- D. (−5, −2)
Choose the right answer
Answer:
4.A(−4, 5) turns about the origin to A′(5, 4). What turn is it?
- A. 90° anticlockwise
- B. A reflection in the x-axis (no turn)
- C. 90° clockwise
- D. 180°
Choose the right answer
Answer:
5.(1, 7) turned 270° anticlockwise about the origin goes to (, ).
Fill in each blank
Answer:

All the answers

1. −9, 5
2. D
3. B. (5, 2)
4. C. 90° clockwise
5. 7, −1

Free worksheet: Rotation about the originWorking out, multiple choice and word problems, with answers and working, to print or save as a PDF

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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