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## Basic geometry and measurement

# Making a scale drawing

CCSS.Math:

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)
- no,

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)

## Video transcript

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.