Resize Both Dimensions Together

Supplied materials

• Paper and a pencil for dimensions and calculations. You can type the calculations instead.
• Read this example: A fictional image is 2 units wide and 3 high. Enlarge both dimensions by factor 2 without distortion. Which dimensions work? Supplied candidates: (A) 2 by 6 (B) 4 by 3 (C) 4 by 5 (D) 4 by 6.
• Try this question: A fictional image is 3 units wide and 4 high. Enlarge both dimensions by factor 3 without distortion. Which dimensions work? Supplied candidates: (A) 3 by 12 (B) 6 by 7 (C) 9 by 12 (D) 9 by 4.

Learn the idea

To enlarge an image without stretching it, multiply its width and height by the same scale factor. Changing only one dimension changes the width-to-height relationship.

Reason through the supplied case: Preserving proportions multiplies both dimensions by the same factor: width 2×2=4, height 3×2=6. Scaling just one dimension changes the width-to-height relationship.

Adding the same number to both dimensions usually changes proportions. Use one multiplicative factor, and distinguish undistorted resizing from a deliberate cropped composition.

1. Read the image dimensions and scale factor. Find the width and height you must multiply.
2. Show how multiplying both 2 and 3 by 2 gives a 4-by-6 image with the same proportions.
3. Try the question and all three practice questions before checking their answers.
4. Resize a four-by-six image by factor three and show both dimension calculations.
5. Check your work: The new dimensions are twelve by eighteen and the width-to-height ratio remains four to six.

Check your reasoning

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Take it further

Try one more question: A fictional image is 3 units wide and 6 high. Enlarge both dimensions by factor 3 without distortion. Which dimensions work? Supplied candidates: (A) 3 by 18 (B) 6 by 9 (C) 9 by 18 (D) 9 by 6. Answer: 9 by 18. Preserving proportions multiplies both dimensions by the same factor: width 3×3=9, height 6×3=18. Scaling just one dimension changes the width-to-height relationship. Now make your own work: Resize a four-by-six image by factor three and show both dimension calculations. Check your work: The new dimensions are twelve by eighteen and the width-to-height ratio remains four to six.

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