Question

the distance formula is equivalent to the pythagorean theorem if you are trying to find the distance between a point in the plane and the orgin is this true or false???

Answer 1

the answer to this is true for apex

Answer 2

Let the point be (x,y) and the origin is (0,0).

Distance formula is

$d = \sqrt{ (x_{2} - x_{1})^2 + ( y_{2} - y_{1})^2}$

Substituting the points,we will get

$d = \sqrt{ (0-x)^2 + (0-y)^2 } \\ d = \sqrt{x^2 +y^2}$

Squaring both sides

$d^2 = x^2 + y^2 \\ x^2 + y^2 = d^2$

And the pythagorean theorem is

$a^2 +b^2 = c^2$

And the above equation we obtained in in the form of pythagorea identity .

So the given statement is true .