If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

### Course: 8th grade (Eureka Math/EngageNY)>Unit 7

Lesson 3: Topic C: The Pythagorean theorem

# 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?
• One simple option is to draw a graph on a sheet of paper, plot your points on it and go from there:)
• 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.)
• At , 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?
• The principal root as sometimes mentioned in some of Sal's videos is basically the positive square root of a number
(1 vote)
• How do you write these answers in decimals?
• for fractions, multiply the numerator by the denominator
(1 vote)
• what is a principle root? As Jimmy Chimichanga said.
• what if its a line going say from (-4,2) to (-4,-4)
• 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.
• 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.