Basic geometry and measurement
Making a scale drawing
An urban planner needs your help in creating a scale drawing. Let's use our knowledge about scale factor, length, and area to assist. Created by Sal Khan.
Want to join the conversation?
- why would u need to have scaled drawings in real life.(16 votes)
- Or if you have a job that requires you to create a model, such as a scientist, an engineer, or an architect.(4 votes)
- I am confused, isn't the area equal to length times width, why did Sal write it as length times length?(6 votes)
- Because it is a square, the length is the same as the width.(3 votes)
- How come there's no video for the construct a scale drawing?(8 votes)
- There is a video called "Make a Scale Drawing" that is for constructing scale drawings(0 votes)
- Is there any tool we can use, like a graph of some sort to help us(3 votes)
- You can use graph paper to help you make scale drawings.
Plot a rectangle on a piece of graph paper at these coordinates:
A(0,0) B(0,2) C(3,2) D(3,0)
Now choose your scale factor. For our example, let's say the scale factor is 4.
To graph the new rectangle, multiply each coordinate by 4 to get:
A(0,0) x 4 = A'(0,0)
B(0,2) x 4 = B'(0,8)
C(3,2) x 4 = C'(12,8)
D(3,0) x 4 = D'(12,0)
You now have a new rectangle that is a scale factor of 4 of the original rectangle.
Try graphing the following triangle on your own:
A(0,0) B(3,2) C(4,0)
Now using a scale factor of 2, graph the new coordinates.
Here is something that is really cool. Did you notice anything about the original points and the new points? Pick any coordinate and it's matching scaled coordinate and draw a line connecting them. If you make the line long enough, all of the lines go through the origin!
Great question and hope this helps <|:)(7 votes)
- How do you do this
it is so confusing(3 votes)
- Scale factor = Dimension of the new shape ÷ Dimension of the original shape?(1 vote)
dimension of new shape= dimension of original x scale factor(4 votes)
- How can you find the area by doing length times length? Isn't it supposed to be length times width?(3 votes)
- its because it is a square and all the sides are equal(0 votes)
- this is confusing(2 votes)
- yes because it is a square you need to do the same to all sides.(2 votes)
- I have a question where you have to move a triangle and it says that the unit is 10m and the height is 15m, I don't know what to do?(2 votes)
Cole is an urban planner. He wants to create a small scale drawing of a city block. The block is a square with an area of 8,100 square meters. Create a scale drawing of the block using a scale factor of 0.1. So the first thing we could think about, they give us the area of the block. And it's a square block. So it has the same length and width. So we could use that information to figure out the length and width of that block. So if it's a square, so let's imagine a square block right over here. And that this is, I guess we could call that the length. And then this is also going to be the length. It's going to be the same dimensions. We know that the area is just going to be the length times the length is going to be equal to 8,100. Or we could say that our length squared is going to be equal to 8,100. So what times itself is equal to 8,100? Well, the 81 might jump out at you. We know that 9 times 9 is equal to 81. But then we have these two zeroes right over here. But if we give each of these nines a zero, then we'll end up with two zeros in the product. So 90 times 90 is equal to 8,100. So now we know the dimensions of this square block. It's a 90 meter by 90 meter square block. It's my best attempt to draw a square block. Now that's the actual square block. Here let me draw it a little bit more like a square. My first drawing looked a little bit too much like a rhombus. So here you go. A little bit better attempt at a square. Now we want to create at a scale drawing of the block using a scale factor of 0.1. So the actual block, once again, is 90 meters by 90 meters. But in our scale drawing, and I'll do this in this purple color, we essentially want each of the dimensions to be 1/10 of their original dimensions. So we could take the scale factor and multiply it by each of these dimensions right over here. So 90 times 0.1, well that's just going to be 9. This right over here is a 1/10. A 1/10 of 90 meters is going to be 9 meters. And so this, when we draw the scale drawing at the scale that Cole intends to draw it at, we would draw 9 meters by 9 meters. And so let's go to the actual tool and draw a 9 meter by 9 meter square, or a 9 by 9 square. We can assume that the units here are in terms of meters. So let's see. I could draw in that dimension. OK, a 9 there. Let me use my mouse instead of my pen tool. It'll be easier. And then let me make this 9, this side 9, and then I could make this side 9. And then we are all set. It's a square. We see we have four right angles. And now we can check our answer. And we got it right.