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

In brief, apply the pythagorean theorem to show that the distance between the point
`(√(2)/2,√(2)/2)` and the origin is
`1`.

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
`(√(2)/2,√(2)/2)` is on the unit circle, show that the distance between
`(√(2)/2,√(2)/2)` and
`(0,0)` equals to
`1`.

What's the distance between
`(√(2)/2,√(2)/2)` and
`(0,0)`?

`\displaystyle \sqrt{\left((√(2))/(2)-0}\right)^(2) + \left((√(2))/(2)-0\right)^(2)} = \sqrt{(1)/(2) + (1)/(2)}= √(1)= 1`.

By the pythagorean theorem, the distance between
`(√(2)/2,√(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
`(√(2)/2,√(2)/2)` is on the unit circle.