Main content

# Finding distance with Pythagorean theorem

Sal finds the distance between two points with the Pythagorean theorem.

## Want to join the conversation?

- So, how do you find the distance between two points, if it isn't on a graph?(18 votes)
- One simple option is to draw a graph on a sheet of paper, plot your points on it and go from there:)(6 votes)

- I have to work in Aleks but in Aleks, they don't give you a numbered graph they just give you the line my work is something like this

Find the distance between the points A and B given below.

(That is, find the length of the segment connecting Aand B.)

Round your answer to the nearest hundredth.(9 votes) - At3:00, what is a principle ( or principal?) root? I have dealt with square roots many times, but is there a difference between a principle root and a square root?(6 votes)
- yes there is a difference the principal root is always positive -2*-2=4 and 2*2=4 the principal root would be 2(1 vote)

- How do you write these answers in decimals?(5 votes)
- what is a principle root? As Jimmy Chimichanga said.(4 votes)
- what if its a line going say from (-4,2) to (-4,-4)(3 votes)
- In that case, you don't need to use the pythagorean theorem. If the x-coordinate of the endpoints is the same, the line is vertical (horizontal if y is same). You can just find how much the y-value increases or decreases from one point to the next, and that's your distance. If you use the pythagorean, one of your side lengths would be 0, so you would have:

(0)^2 + (2 - (-4))^2 = c^2

6^2 = c^2

c = 6

So the distance would be 6 units.(2 votes)

- I thought there was another way to find the distances between two points? I learned √ (x2 − x1)2 + (y2 − y1)2

The two 2 outside means squared.(3 votes) - On2:19How Do You Solve For C?(2 votes)
- Replying to put it in leymans terms.

c^2=a^2+b^2. To find the exact number for c^2, you'll need to find the SQUARE ROOT of that number.

Heres an example:

5^2+5^2 is equivalent to C^2

=25+25 is c^2

50=c^2

square root of 50=c(1 vote)

- I am confusion!how do's you do this?!america explain!(2 votes)
- Why do we have to put the coordinates? Is it optional?(1 vote)

## Video transcript

- We are asked what is the distance between the following points. Pause this video and see
if you can figure it out. There's multiple ways to think about it. The way I think about it
is really to try to draw a right triangle where these points, where the line that connects
these points is the hypotenuse and then we can just use
the Pythagorean Theorem. Let me show you what I am talking about. Let me draw a right triangle, here. That is the height of my right triangle and this is the width
of my right triangle. Then the hypotenuse will
connect these two points. I could use my little
ruler tool here to connect that point and that
point right over there. I'll color it in orange. There you have it. There you have it. I have a right triangle
where the line that connects those two points is the
hypotenuse of that right triangle. Why is that useful? From this, can you pause
the video and figure out the length of that orange
line, which is the distance between those two points? What is the length of this red line? You could see it on this grid, here. This is equal to two. It's exactly two spaces, and
you could even think about it in terms of coordinates. The coordinate of this point up here is negative five comma eight. Negative five comma eight. The coordinate here is
X is four, Y is six. Four comma six, and so
the coordinate over here is going to have the same
Y coordinate as this point. This is going to be comma six. It's going to have the same
X coordinate as this point. This is going to be
negative five comma six. Notice, you're only
changing in the Y direction and you're changing by two. What's the length of this line? You could count it out, one, two, three, four, five, six, seven, eight, nine. It's nine, or you could even say hey look, we're only changing in the X value. We're going from negative five, X equals negative five, to X equals four. We're going to increase by nine. All of that just sets us up so that we can use the Pythagorean Theorem. If we call this C, we know
that A squared plus B squared is equal to C squared, or we
could say that two squared ... Let me do it over here. Use that same red color. Two squared plus nine
squared, plus nine squared, is going to be equal to
our hypotenuse square, which I'm just calling C, is
going to be equal to C squared, which is really the distance. That's what we're trying to figure out. Two squared, that is four,
plus nine squared is 81. That's going to be equal to C squared. We get C squared is equal to 85. C squared is equal to 85 or C is equal to the principal root of 85. Can I simplify that a little bit? Let's see. How many times does five go into 85? It goes, let's see, it goes 17 times. Neither of those are perfect squares. Yeah, that's 50 plus 35. Yeah, I think that's about
as simple as I can write it. If you wanted to express it as a decimal, you could approximate it by
putting this into a calculator and however precise you want
your approximation to be. That over here, that's
the length of this line, our hypotenuse and our right triangle, but more importantly for
the question they're asking, the distance between those points.