To calculate the distance between two points \((x_1, y_1)\) and \((x_2, y_2)\):
\[ D = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
Where:
The distance between two points on a coordinate plane is the length of the straight line connecting them. This distance is calculated using the Euclidean distance formula, which is derived from the Pythagorean theorem. The formula measures the straight-line distance between two points by taking the square root of the sum of the squares of the differences in their coordinates.
Example 1:
Assume the following coordinates:
Using the formula:
\[ D = \sqrt{(4 - 1)^2 + (6 - 2)^2} = \sqrt{3^2 + 4^2} = \sqrt{9 + 16} = \sqrt{25} = 5 \]
The distance between the points is 5 units.
Example 2:
Assume the following coordinates:
Using the formula:
\[ D = \sqrt{(2 - (-1))^2 + (2 - (-2))^2} = \sqrt{3^2 + 4^2} = \sqrt{9 + 16} = \sqrt{25} = 5 \]
The distance between the points is 5 units.