Unit 6 Lesson 7 Pythagorean Theorem in Three Dimensions Quick Check

Answer 1

1. What does the Pythagorean theorem state?
- The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides.

2. How can the Pythagorean theorem be applied in three dimensions?
- In three dimensions, the Pythagorean theorem can be used to find the distance between two points in space. By considering the x, y, and z coordinates as the sides of a right-angled triangle, the Pythagorean theorem can be applied to calculate the distance between the two points.

3. How do you calculate the distance between two points in a three-dimensional space using the Pythagorean theorem?
- To calculate the distance between two points (x1, y1, z1) and (x2, y2, z2) in three-dimensional space, you can use the formula:
√((x2-x1)^2 + (y2-y1)^2 + (z2-z1)^2)

4. If point A has coordinates (2, 3, 4) and point B has coordinates (5, 1, 6), what is the distance between the two points?
- Using the formula above:
√((5-2)^2 + (1-3)^2 + (6-4)^2)
= √(3^2 + (-2)^2 + 2^2)
= √(9 + 4 + 4)
= √17

Therefore, the distance between points A and B is √17 units.