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 = √( (0-x)^2 + (0-y)^2 ) \\ d = √(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 .