Question

what is the distance betwen the points (8,3) and (2,0), using the distance formula?

Answer 1

\[d = \sqrt{(x_2-x_1)^2+(y_2 - y_2)^2}\]

Answer 2

@Gir_le
Use the above formula.

Answer 3

If you know the pythagorean theorem, you never need to memorize the distance formula because they are the same thing. Look at the attached picture for reference.
You can draw a right triangle and then figure out the length of the hypotenuse from the length of the legs.

Answer 4

@smooth math-
Can you use the pythagorean theory method if you don't have a graph for the points?

Answer 5

Yes you can. You just need to figure out the legs of the triangle, but one leg is the difference in x and the other leg is the difference in y.

Answer 6

The graph just helps you to see why it works.

Answer 7

can you show me useing these two points, please?

Answer 8

I'll use two different points so you can see how it's done and do the problem on your own.

Answer 9

kk, tx!

Answer 10

Consider the point (2,6) and (5, 10).

Okay, well there is a triangle and we want to find the hypotenuse.
One leg is the difference in the xs of the points. One has x 5 and the other has x 2, so the difference is 5-2 = 3.
The other leg is the difference in y, which is 10 -6 = 4.

By the pythagorean theorem, if the hypotenuse is c and the legs are a and b, then c^2 =a^2 +b^2
Which means c = sqrt(a^2 + b^2)
a and b are 3 and 4, so
c = sqrt(3^2 + 4^2) = sqrt(9 + 16) = sqrt(25) = 5

Answer 11

Understand?

Answer 12

yeah... i had to read that a couple hundred times to get it but i uinderstand now. thanks! :)

Answer 13

Haha sorry I couldn't explain it more simply, but thank you for putting in the effort to understand it =) Good job.