How can I check whether a scale factor enlarges or shrinks a drawing?
Quick answer
First identify the original drawing and the changed image. For a scale factor defined as image length ÷ original length, a factor greater than 1 means the image enlarges, a factor between 0 and 1 means it shrinks, and 1 means corresponding lengths stay the same. Check the labels before interpreting the factor: reversing the ratio reverses what the number tells you.
The question, the details, the next step.
I need to decide whether a drawing gets bigger or smaller before I work out all its new lengths. What should I check first?
Start by naming the two figures: which is the original, and which is the image after scaling? Then look at the scale factor’s order. If it is defined as image length divided by corresponding original length, compare it with 1: greater than 1 predicts an enlargement; between 0 and 1 predicts a shrink; exactly 1 predicts no change in corresponding lengths. This ratio-based check follows the idea that a scale factor compares corresponding measurements of an object and its image. [S1]
Do this before multiplying any side lengths. It is a direction check, not a substitute for checking that the right sides or other corresponding measurements are being compared.
How do I know whether the factor is image ÷ original or original ÷ image? My worksheet just says the scale factor is 0.6.
Look for the worksheet’s definition, an arrow showing the change, or a worked example. The number alone is not enough to tell you which direction it describes: a factor compares two measurements, so you need to know which one is on top. The source explains the ratio framework but does not establish how your particular worksheet defines its factor. [S1]
If the worksheet says “multiply the original by 0.6 to get the image,” then 0.6 is image ÷ original, so the image shrinks. If it defines the ratio in the reverse order, do not apply that conclusion to the original-to-image change without reversing the ratio. If the convention remains unclear, ask your teacher or write down your interpretation before calculating.
Can you show the check with an actual length, including a factor bigger than 1?
Assume a rectangle’s original long side is 8 cm, and the stated factor means image ÷ original.
- With a factor of 0.6, the direction check says shrink, because 0.6 is between 0 and 1. The image side would be 8 × 0.6 = 4.8 cm.
- With a factor of 1.5, the check says enlarge, because 1.5 is greater than 1. The image side would be 8 × 1.5 = 12 cm.
- With a factor of 1, the side stays 8 cm.
The arithmetic confirms the prediction, but the prediction comes from comparing the factor with 1. For similar figures, corresponding side lengths are proportional; this example assumes the stated factor applies to corresponding lengths. [S1] Check the assignment’s wording to confirm its factor convention.
What’s a quick way to avoid mixing up the labels or making a direction mistake when I solve another one?
Write the ratio with words before substituting numbers: “image ÷ original = factor.” Then test whether that factor would make a sample original length larger or smaller when multiplied. For example, multiplying a positive length by 0.6 makes the result smaller, which agrees with the shrink prediction. Keep the original and image labels beside your measurements, and compare matching sides rather than unrelated sides. The factor’s direction depends on which figure is identified as the original and which as the image. [S1]
A reusable setup is: “Original = [length and unit]. Image = [length and unit]. Factor definition = [image ÷ original or other stated order]. Compare factor with 1: [greater than / between 0 and 1 / equal]. Predicted change = [enlarge / shrink / unchanged].” Fill that in before calculating every new side.
A practical checklist
Label the starting drawing “original” and the changed drawing “image.”
Write the factor’s order in words, such as image ÷ original.
Compare the factor with 1 before calculating lengths.
Match corresponding sides or measurements, not unrelated ones.
Check whether a sample multiplication agrees with your predicted direction.
A few more useful answers
If the factor is 1, is the drawing enlarged or shrunk?
Neither: corresponding lengths stay the same when the image-to-original factor is 1.
Can I decide from the number alone?
Only if you know how the factor is defined. A value such as 0.6 indicates shrinkage when the factor is image ÷ original; a reversed ratio needs a different interpretation.
Does this check tell me every new side length?
No. It predicts the direction of change. To find a new length, use the stated factor with the matching original length and follow the factor convention in the problem.
Sources
References used for this guide.
- [S1] OpenStax Contemporary Mathematics: Triangles and Similarity openstax.org · Checked