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)