Pythagorean Theorom and Distance Formula?

Question

How are the Pythagorean Theorom and Distance Formula related? What are the similarities between the two? What are the differences between the two?

Answer 1

The Pythagorean theorem and the distance formula are exactly the same thing, just that for the distance formula you need to find the change in x and the change in y.
In Pythagoras we have:
a^2+b^2=c^2
In the distance formula we need to find the change in x: (x1-x2) and that becomes our new a. Same thing with y: (y1-y2), and that is our new b. C is the distance. so basically what we have after substituting is:
(x1-x2)^2+(y1-y2)^2= C^2
and by taking the square root of both sides we end up with
_____________________
sqrt.V(x1-x2)^2+(y1-y2)^2= C^2

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sqrt.V(x1-x2)^2+(y1-y2)^2= C

Answer 2

Pythagorean Theorem related to all three sides of the right triangle. The lengths of two sides must be known in order to solve pythagorean Theorem.

The distance formula relates to the coordinates plane of the x axis and y axis

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Answer 3

they both use to find a length of a side

difference is that Pythagorean is used in a right triangle and Distance formula is used by using coordinates.

Answer 4

consider triABC

ca^2=ab^2+cb^2

if u want the length of ca then
it's distance given by (ab^2+cb^2)^1/2
here u will be knowing the length of two other sides wrt to this sides u will find the distance of ca

which is same as distance formula.
here u will be knowing the co ordinates .


if u couldn't understand i could explain more in detail the problem is i don't have pen and paper

Answer 5

Draw a line between the two points. Now draw a line across from one point and up/down from the other. They will intersect giving you a right-angled triangle. Apply Pythagoras's theorm to the triangle to get the distance formula.

How do they differ? One is a formula, the other is a theorem.