A scale copy has every length multiplied by the same number. That number is the scale factor.
Scale factor is the number every length is multiplied by to make the copy.
Step 1: Let's Learn
Read it, or press Listen and follow the words.
Every length, not some
If one side doubles and another triples, the result is a distortion, not a scale copy.
Angles do not change
Scaling changes lengths but leaves every angle exactly as it was.
A factor under 1 shrinks
A scale factor of 1/2 makes a copy half the size. It is still a scale copy.
What makes a copy a scale copy
A scale copy has all its lengths multiplied by the same number and all its angles unchanged. Both conditions matter. Stretch a photo horizontally only and the angles change — the result is a distortion, not a scale copy.
The scale factor
The number every length is multiplied by is the scale factor. A factor above 1 enlarges, below 1 shrinks, and exactly 1 leaves the figure unchanged. To find it, divide a length on the copy by the matching length on the original.
Testing whether two figures are scale copies
Divide each pair of matching lengths. If every division gives the same number, the figures are scale copies; if the ratios differ, they are not. One inconsistent pair is enough to rule it out.
Match the parts before dividing
The longest side of the original corresponds to the longest side of the copy, and so on. Dividing mismatched sides gives a meaningless ratio. On a rotated or reflected copy the matching is not obvious, so identify corresponding parts first.
Step 2: Try It Yourself
Tap and try it out.
| Original | Copy |
|---|---|
| 3 | 6 |
| 6 | 12 |
Every row is the same ratio. 3 to 6 is the same comparison as 6 to 12.
Step 3: Watch an Example
One step at a time.
Watch Ana Find a Scale Factor
A rectangle 4 by 6 is copied as 10 by 15.
- Step 1
She compares matching sides: 4 became 10.
Step 4: Your Turn
Practice makes it stick.
The Photo
Problem 1 of 2
A 5 cm side is scaled by 4. How long is the copy?
cm
The Map
Problem 2 of 2
A 12 cm side becomes 3 cm. What is the scale factor, as a bottom number of a fraction with top 1?
Scale It
1 of 4
A 7 cm side scaled by 3. How long is the copy?
2 of 4
A 6 cm side becomes 18 cm. What is the scale factor?
3 of 4
A 20 cm side scaled by 1/2. How long is the copy?
4 of 4
Do angles change when a shape is scaled?
Step 5: Quick Check
Show what you know.
Question 1 of 2
A 9 cm side becomes 27 cm. What is the scale factor?
Question 2 of 2
What makes a copy a scale copy?
What You Learned
- A scale copy multiplies every length by the same factor.
- Angles stay exactly the same.
- A factor under 1 shrinks and still counts as a scale copy.