What happens to a point rotated 90° counter-clockwise about the origin?

(x, y) becomes (−y, x). A 180° rotation gives (−x, −y), and 270° counter-clockwise gives (y, −x).

How do I print or save these worksheets as a PDF?

Click Print worksheet and choose your printer, or pick “Save as PDF” as the destination to keep a digital copy. The answer key prints on its own page.

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Yes. Click New problems for a brand new randomly generated worksheet, as many times as you like.

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Transformations worksheet generator

Coordinate transformation practice. Students apply a translation, reflection, rotation about the origin, or dilation to a point.

Transformations

Name: Date:

1.
Reflect (10, -4) across the y-axis.
2.
Translate (1, -3) by (6, 10).
3.
Dilate (7, -1) by a scale factor of 5, centred at the origin.
4.
Translate (10, 3) by (-1, -4).
5.
Rotate (6, 8) 270° counter-clockwise about the origin.
6.
Reflect (6, 3) across the x-axis.
7.
Dilate (-4, -6) by a scale factor of 2, centred at the origin.
8.
Rotate (-5, -9) 270° counter-clockwise about the origin.
9.
Translate (-3, -6) by (4, 6).
10.
Rotate (-9, 2) 270° counter-clockwise about the origin.
11.
Dilate (-10, 1) by a scale factor of 4, centred at the origin.
12.
Reflect (7, -1) across the x-axis.
13.
Reflect (1, 5) across the x-axis.
14.
Dilate (7, -1) by a scale factor of 2, centred at the origin.
15.
Dilate (-10, -7) by a scale factor of 3, centred at the origin.
16.
Translate (5, -1) by (-3, 10).
17.
Reflect (10, 6) across the x-axis.
18.
Rotate (2, -7) 90° counter-clockwise about the origin.
19.
Translate (7, 9) by (6, -4).
20.
Translate (6, 10) by (8, 9).

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Transformations — Answer Key

Name: Date:

1.
Reflect (10, -4) across the y-axis.
(-10, -4)
2.
Translate (1, -3) by (6, 10).
(7, 7)
3.
Dilate (7, -1) by a scale factor of 5, centred at the origin.
(35, -5)
4.
Translate (10, 3) by (-1, -4).
(9, -1)
5.
Rotate (6, 8) 270° counter-clockwise about the origin.
(8, -6)
6.
Reflect (6, 3) across the x-axis.
(6, -3)
7.
Dilate (-4, -6) by a scale factor of 2, centred at the origin.
(-8, -12)
8.
Rotate (-5, -9) 270° counter-clockwise about the origin.
(-9, 5)
9.
Translate (-3, -6) by (4, 6).
(1, 0)
10.
Rotate (-9, 2) 270° counter-clockwise about the origin.
(2, 9)
11.
Dilate (-10, 1) by a scale factor of 4, centred at the origin.
(-40, 4)
12.
Reflect (7, -1) across the x-axis.
(7, 1)
13.
Reflect (1, 5) across the x-axis.
(1, -5)
14.
Dilate (7, -1) by a scale factor of 2, centred at the origin.
(14, -2)
15.
Dilate (-10, -7) by a scale factor of 3, centred at the origin.
(-30, -21)
16.
Translate (5, -1) by (-3, 10).
(2, 9)
17.
Reflect (10, 6) across the x-axis.
(10, -6)
18.
Rotate (2, -7) 90° counter-clockwise about the origin.
(7, 2)
19.
Translate (7, 9) by (6, -4).
(13, 5)
20.
Translate (6, 10) by (8, 9).
(14, 19)

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Frequently asked questions

What happens to a point rotated 90° counter-clockwise about the origin?: (x, y) becomes (−y, x). A 180° rotation gives (−x, −y), and 270° counter-clockwise gives (y, −x).
How do I print or save these worksheets as a PDF?: Click Print worksheet and choose your printer, or pick “Save as PDF” as the destination to keep a digital copy. The answer key prints on its own page.
Can I get a fresh set of problems?: Yes. Click New problems for a brand new randomly generated worksheet, as many times as you like.
Is this worksheet generator free?: Yes. Every generator on the site is free to use, with no account, no watermark and unlimited printing for classroom or home use.