Question

what are the similarities in the pythagorean theorem and the distance formula

Answer 1

Answer:

The Pythagorean theorem states that, for all 90-degree triangles, the relationship between the lengths of the sides is given by the formula a^2 + b^2 = c^2.

DISTANCE FORMULA

The study of geometry in a graphical environment is called co-ordinate geometry.

In co-ordinate geometry, the standard formula for calculating the distance between 2 points is called the distance formula.

Step-by-step explanation:

Answer 2

Answer:

Short answer: They are essentially the same thing.

The distance formula is derived from the Pythagorean Theorem

We have distance formula:

$D = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}$

Pythagorean Theorem:

$a^2+b^2=c^2 \Rightarrow c=\sqrt{a^2+b^2}$

The shortest distance between two points if a line. If you draw a line in the cartesian plane both points will have an x-coordinate and y-coordinate. Note that it forms a right triangle! Therefore, the distance between those points is the hypotenuse.

We can have a point $a=(x_{1}, y_{1})$ and point $b=(x_{2}, y_{2})$

But once $a$ and $b$ can be positive or negative:

$c = \sqrt{a^2+b^2}= D = \sqrt{(\pm a)^2+(\pm b)^2}$