Question

ASAP!!! Use the pythagorean theorem to prove that the point (√2/2, √2/2) lies on the unit circle. I need setup, explination, answer

Answer 1

Answer:

In brief, apply the pythagorean theorem to show that the distance between the point $(\sqrt{2}/2,\sqrt{2}/2)$ and the origin is $1$.

Step-by-step explanation:

The pythagorean theorem can give the distance between two points on a plane if their coordinates are known.

A point is on a circle if its distance from the center of the circle is the same as the radius of the circle.

On a cartesian plane, the unit circle is a circle  

• centered at the origin $(0,0)$
• with radius $1$.

Therefore, to show that the point $(\sqrt{2}/2,\sqrt{2}/2)$ is on the unit circle, show that the distance between $(\sqrt{2}/2,\sqrt{2}/2)$ and $(0,0)$ equals to $1$.

What's the distance between $(\sqrt{2}/2,\sqrt{2}/2)$ and $(0,0)$?

$\displaystyle \sqrt{\left(\frac{\sqrt{2}}{2}-0}\right)^{2} + \left(\frac{\sqrt{2}}{2}-0\right)^{2}} = \sqrt{\frac{1}{2} + \frac{1}{2}}= \sqrt{1}= 1$.

By the pythagorean theorem, the distance between $(\sqrt{2}/2,\sqrt{2}/2)$ and the center of the unit circle, $(0,0)$, is the same as the radius of the unit circle, $1$. As a result, the point $(\sqrt{2}/2,\sqrt{2}/2)$ is on the unit circle.