Distance and the pythagorean theorem quick check
1. What is the Pythagorean Theorem?
The Pythagorean Theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
2. How can the Pythagorean Theorem be used to find the distance between two points in a coordinate plane?
To find the distance between two points (x1, y1) and (x2, y2) in a coordinate plane, you can use the Pythagorean Theorem. The difference in x-coordinates and the difference in y-coordinates represent the lengths of the two legs of a right-angled triangle. The distance between the two points is then the square root of the sum of the squares of these differences.
Distance = √((x2 - x1)^2 + (y2 - y1)^2)
3. How can the Pythagorean Theorem be used to find the diagonal of a rectangle?
To find the diagonal of a rectangle, you can use the Pythagorean Theorem. The length and width of the rectangle represent the lengths of the two legs of a right-angled triangle. The diagonal of the rectangle is then the square root of the sum of the squares of these lengths.
Diagonal = √(length^2 + width^2)
4. How can the Pythagorean Theorem be used to find the distance between two points in a three-dimensional space?
In three-dimensional space, to find the distance between two points (x1, y1, z1) and (x2, y2, z2), you can use an extension of the Pythagorean Theorem. The difference in x-coordinates, the difference in y-coordinates, and the difference in z-coordinates represent the lengths of the three sides of a right-angled triangle. The distance between the two points is then the square root of the sum of the squares of these differences.
Distance = √((x2 - x1)^2 + (y2 - y1)^2 + (z2 - z1)^2)