Free printable resources · Original practice
Rotate each original figure about the origin, record the rule and check every image vertex rather than estimating the angle by eye.
Free rotation worksheets on a coordinate grid with 90°, 180° and 270° turns. Separate student, reference and answer files in Letter/A4 PDF/SVG.
Choose Letter or A4, then download a student sheet first. Keep the separate reference or answer file closed until you have attempted the case. Every worksheet, SVG and answer is free without signup.
Original worksheet collection. Letter or A4 PDF and editable SVG.
Original worksheet collection. Letter or A4 PDF and editable SVG.
Original worksheet collection. Letter or A4 PDF and editable SVG.
Original worksheet collection. Letter or A4 PDF and editable SVG.
Complete free PDF pack.
| Case | Given information | Task |
|---|---|---|
| RO01 | Vertices in order: A(1, 1); B(4, 1); C(2, 3). | Rotate 90 degrees counterclockwise about (0, 0). Draw and label the image. Check the coordinates of every vertex. |
| RO02 | Vertices in order: A(-3, 1); B(-1, 1); C(-1, 3); D(-3, 3). | Rotate 180 degrees counterclockwise about (0, 0). Draw and label the image. Check the coordinates of every vertex. |
| RO03 | Vertices in order: A(-2, 1); B(1, 1); C(0, 4). | Rotate 270 degrees counterclockwise about (0, 0). Draw and label the image. Check the coordinates of every vertex. |
| RO04 | Vertices in order: A(1, -4); B(4, -4); C(3, -1); D(1, -1). | Rotate 90 degrees counterclockwise about (0, 0). Draw and label the image. Check the coordinates of every vertex. |
Use the coordinates, dimensions and rules given for each case. Distances and areas are measured in grid units.
RO01: Quarter turn left
| Step | Worked result |
|---|---|
| 1 | Rotate 90 degrees counterclockwise about (0, 0). |
| 2 | Image vertices: A(-1, 1); B(-1, 4); C(-3, 2). |
The first case shows the checking pattern. Individual answer files contain the completed graph or net and result for every case.
To rotate a point 90 degrees counterclockwise about the origin, swap its coordinates and change the sign of the new x-coordinate: (x, y) becomes (-y, x). For 180 degrees, change both signs: (x, y) becomes (-x, -y). For 270 degrees counterclockwise, (x, y) becomes (y, -x). Apply the rule to each vertex, then connect the image points in the same order. For example, rotating A(1, 1), B(4, 1), C(2, 3) 90 degrees counterclockwise gives A(-1, 1), B(-1, 4), C(-3, 2). Check that side lengths and angles are unchanged.
Rotation does not change the size or shape of a figure, so the area stays the same. After finding the image vertices, you can verify by computing the area of the original and the image. For a triangle, use the shoelace formula or count grid squares. For example, the triangle with vertices A(1, 1), B(4, 1), C(2, 3) has area 3 square units. Its 90-degree counterclockwise image has vertices A(-1, 1), B(-1, 4), C(-3, 2) and also area 3 square units. If your computed areas differ, recheck the coordinate signs and the order of vertices.
Plot the original vertices on a coordinate grid. Apply the rotation rule to each vertex to get the image coordinates. Plot the image points and connect them in the same order as the original. Label each image vertex with its prime notation, such as A', B', C'. For a 180-degree rotation of A(-3, 1), B(-1, 1), C(-1, 3), D(-3, 3), the image vertices are A'(3, -1), B'(1, -1), C'(1, -3), D'(3, -3). Ensure the image is the same distance from the origin as the original and that corresponding segments are equal in length.
| Watch for | Check instead |
|---|---|
| Applying the 90-degree counterclockwise rule as (x, y) becomes (y, -x). | For 90 degrees counterclockwise, (x, y) becomes (-y, x). For example, (1, 1) becomes (-1, 1), not (1, -1). |
| Assuming that if two lines have slopes whose product is 1, they are parallel. | Parallel lines have equal slopes and different intercepts. A product of 1 does not indicate parallel lines; perpendicular lines have a slope product of -1. |
| Rotating a shape but changing the order of the vertices when connecting them. | Connect the image vertices in the same order as the original vertices to preserve the shape. For example, if original vertices are A, B, C in order, connect A', B', C' in that order. |
Choose the PDF that matches your paper. Print at Actual size / 100% and turn off Fit, Shrink and browser headers. SVG is editable but an editor can rescale it; the PDF is the simpler print route.
Use the rule (x, y) becomes (y, -x). For example, rotating A(-2, 1) 270 degrees counterclockwise gives A'(1, 2).
No. Rotation is a rigid transformation, so area is preserved. For instance, a triangle with area 3 square units still has area 3 square units after any rotation.
Rewrite both equations in slope-intercept form. If the slopes are equal and the y-intercepts are different, the lines are parallel. If both slopes and intercepts are equal, they are the same line.
Yes. The individual student, reference and answer files plus collection packs are free without signup. Credit Zumola under CC BY 4.0 when sharing or adapting.
The diagrams and exercises on this page are original Zumola resources.
