explain the distance formula. then use it to calculate the distance between A(1,1) and B(7,-7). explain in one to two sentences
The distance formula is a mathematical equation used to find the distance between two points in a coordinate plane. It states that the distance between two points (x1, y1) and (x2, y2) is equal to the square root of the sum of the squares of the differences between the corresponding coordinates. By using the distance formula on points A(1,1) and B(7,-7), we can calculate the distance between them, which is 14 units.
The distance formula calculates the distance between two points in a coordinate plane. It can be derived from the Pythagorean theorem and is given by the equation:
d = √((x2 - x1)^2 + (y2 - y1)^2)
Using this formula, the distance between point A(1,1) and point B(7,-7) can be calculated as:
d = √((7-1)^2 + (-7-1)^2) = √(36 + 64) = √100 = 10. The distance is 10 units.
The distance formula calculates the distance between two points in a coordinate plane. To use it, we first determine the difference between the x-coordinates and the difference between the y-coordinates of the two points. Then, we square each difference, add them together, and take the square root of the sum. In this example, the distance between A(1,1) and B(7,-7) is calculated as follows:
1. Find the difference between x-coordinates: 7 - 1 = 6
2. Find the difference between y-coordinates: -7 - 1 = -8
3. Square each difference: 6^2 = 36, (-8)^2 = 64
4. Add the squares of the differences: 36 + 64 = 100
5. Take the square root of the sum: √100 = 10
Therefore, the distance between A(1,1) and B(7,-7) is 10 units.