Free printable resources · Original practice
Draw a scaled copy of each polygon, multiply every length by the factor and check that corresponding angles stay the same.
Free scaled polygon worksheets with rectangles, parallelograms, triangles and trapezoids. Download printable PDF and editable SVG practice and answers.
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 |
|---|---|---|
| SP01 | Vertices in order: A(0, 0); B(4, 0); C(4, 2); D(0, 2). | Dilate about (0, 0) by scale factor 2. Draw and label the image. State the length and area ratios. |
| SP02 | Vertices in order: A(0, 0); B(6, 0); C(8, 3); D(2, 3). | Dilate about (0, 0) by scale factor 1/2. Draw and label the image. State the length and area ratios. |
| SP03 | Vertices in order: A(0, 0); B(2, 0); C(0, 3). | Dilate about (0, 0) by scale factor 3. Draw and label the image. State the length and area ratios. |
| SP04 | Vertices in order: A(0, 0); B(6, 0); C(5, 3); D(1, 3). | Dilate about (0, 0) by scale factor 2/3. Draw and label the image. State the length and area ratios. |
Use the coordinates, dimensions and rules given for each case. Distances and areas are measured in grid units.
SP01: Double a rectangle
| Step | Worked result |
|---|---|
| 1 | Dilate about (0, 0) by scale factor 2. |
| 2 | Image vertices: A(0, 0); B(8, 0); C(8, 4); D(0, 4). |
| 3 | Length ratio = 2; area ratio = 4. Area: 8 to 32 square units. |
The first case shows the checking pattern. Individual answer files contain the completed graph or net and result for every case.
To draw a scaled copy, multiply each vertex coordinate by the scale factor. For the rectangle A(0,0), B(4,0), C(4,2), D(0,2) with factor 2, the image is A(0,0), B(8,0), C(8,4), D(0,4). Connect the vertices in the same order. The length ratio equals the scale factor: 2. The area ratio is the square of the scale factor: 4. The original area is 8 square units, and the image area is 32 square units. Check that corresponding sides are parallel and proportional.
For a scale factor of 1/2 on A(0,0), B(6,0), C(8,3), D(2,3), multiply each coordinate by 1/2 to get A(0,0), B(3,0), C(4,3/2), D(1,3/2). The length ratio is 1/2, and the area ratio is (1/2)^2 = 1/4. The original area is 18 square units, and the image area is 9/2 square units. For a factor of 2/3 on A(0,0), B(6,0), C(5,3), D(1,3), the image vertices are A(0,0), B(4,0), C(10/3,2), D(2/3,2). The length ratio is 2/3, and the area ratio is 4/9. The original area is 15, and the image area is 20/3.
After dilating, verify that every side length is multiplied by the scale factor. For the triangle A(0,0), B(2,0), C(0,3) with factor 3, the image is A(0,0), B(6,0), C(0,9). The original area is 3 square units, and the image area is 27 square units. The length ratio is 3, and the area ratio is 9. Use the area ratio to confirm: (scale factor)^2 = area ratio. For factor 2, area ratio is 4; for 1/2, area ratio is 1/4; for 3, area ratio is 9; for 2/3, area ratio is 4/9. Always state both ratios clearly.
| Watch for | Check instead |
|---|---|
| Multiplying only one coordinate of each vertex by the scale factor. | Multiply both x and y coordinates of every vertex by the scale factor. For example, B(4,0) with factor 2 becomes B(8,0), not B(8,0) with y unchanged incorrectly. |
| Using the scale factor as the area ratio. | The area ratio is the square of the scale factor. For factor 2, area ratio is 4; for factor 1/2, area ratio is 1/4; for factor 3, area ratio is 9; for factor 2/3, area ratio is 4/9. |
| Connecting image vertices in a different order than the original. | Connect the image vertices in the same order as the original polygon. For A(0,0), B(4,0), C(4,2), D(0,2) with factor 2, connect A(0,0) to B(8,0) to C(8,4) to D(0,4) and back to A. |
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Multiply each coordinate of every vertex by the scale factor. For A(0,0), B(4,0), C(4,2), D(0,2) with factor 2, the image is A(0,0), B(8,0), C(8,4), D(0,4).
The area ratio is the square of the scale factor. For factor 2, area ratio is 4; for factor 1/2, area ratio is 1/4; for factor 3, area ratio is 9; for factor 2/3, area ratio is 4/9.
Check that each side length is multiplied by the scale factor and that the area ratio equals the square of the scale factor. For the triangle with factor 3, original area 3 becomes 27, and length ratio is 3.
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