A plan is drawn at 1 cm to 2 m. You need the same room at 1 cm to 4 m.
Step 1: Let's Learn
Read it, or press Listen and follow the words.
Go through the real length
Convert the old drawing to the real size first, then convert that down to the new drawing.
With those numbers
6 cm at 1 : 2 is 12 m. At 1 cm to 4 m, 12 m becomes 3 cm.
Does that make sense
Each centimetre now covers twice as much ground, so the drawing is half the size. It should shrink.
Changing the scale of a drawing
To redraw at a new scale, find the ground measurements from the original drawing, then apply the new scale to each. Going through the real dimensions avoids compounding the two scales incorrectly.
Or work out a single factor
Going from 1 : 100 to 1 : 50 doubles every length on the drawing, because the new scale shows things at twice the size. One factor applied to every measurement is quicker, provided you get the direction right.
Angles never change
Rescaling multiplies lengths and leaves every angle exactly as it was. If an angle changes, the new drawing is not a scale copy. This is the same defining property from the first lesson of the chapter, now used as a check.
The area changes by the square
Doubling every length on a redrawn plan quadruples the area of the drawing, even though the building it represents is unchanged. Keeping clear about which area you mean — drawing or ground — prevents a confusing kind of error.
Step 2: Try It Yourself
Tap and try it out.
Before: 6
After: 3
The factor is less than 1, so the bar got shorter. Multiplying does not always make things bigger.
Step 3: Watch an Example
One step at a time.
Watch Leo Redraw a Plan
A wall is 8 cm long at 1 cm to 3 m. Leo redraws it at 1 cm to 6 m.
- Step 1
He finds the real length first: 8 × 3 = 24 m.
Step 4: Your Turn
Practice makes it stick.
The Redraw
Problem 1 of 2
10 cm at 1 cm to 2 m. What is the real length, in metres?
The New Plan
Problem 2 of 2
That same 20 m, drawn at 1 cm to 5 m. How many cm?
From One Scale to Another
1 of 4
6 cm at 1 cm to 4 m. Real length in metres?
2 of 4
That 24 m at 1 cm to 8 m. Drawing length in cm?
3 of 4
5 cm at 1 cm to 10 m, redrawn at 1 cm to 5 m. New length in cm?
4 of 4
If each centimetre covers more ground, does the drawing get bigger or smaller? Answer 1 for bigger, 2 for smaller.
Step 5: Quick Check
Show what you know.
Question 1 of 1
9 cm at 1 cm to 2 m, redrawn at 1 cm to 3 m. New length in cm?
What You Learned
- To change scale, go through the real length.
- Old drawing to real, then real to new drawing.
- A scale covering more ground per centimetre makes a smaller drawing.