# Problem Set 3

How can we use the Pythagorean Theorem in 3-space?

## 1. With the following sets of numbers, find the square root of the sum of their squares.

a) 1 and 2 b) 2 and 3 c) 4 and 4 d) 1 and 4

## 2. With the following sets of numbers, find the square root of the sum of their squares.

a) and 2 b) and 6 c) and 7 d) and 8 Do see any patterns or have any conjectures? Explain your thought process.

## 3. How could we find the distance from the origin to the following points in three-space? Calculate each of them before testing them out in Geogebra. Were your conjectures holding true?

(You will need to test out your calculations in the next worksheet, where a point is set by sliders *a*, *b*, and *c*, and the distance is automatically calculated in three dimensions.)
a) (1, 2, 2)
b) (2, 3, 6)
c) (4, 4, 7)
d) (1, 4, 8)