About Distance Between Two Points
What is the Distance Between Two Points?
The distance between two points is the length of the straight line segment connecting them in a two-dimensional plane.
Formula for Distance Between Two Points
The distance \(d\) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by:
\[d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\]
Where:
- \((x_1, y_1)\) are the coordinates of the first point
- \((x_2, y_2)\) are the coordinates of the second point
- \(d\) is the distance between the two points
Calculation Steps
- Identify the coordinates of both points: \((x_1, y_1)\) and \((x_2, y_2)\)
- Calculate the difference in x-coordinates: \((x_2 - x_1)\)
- Calculate the difference in y-coordinates: \((y_2 - y_1)\)
- Square both differences
- Add the squared differences
- Take the square root of the sum
Example
Let's calculate the distance between points A(1, 2) and B(4, 6):
- \(x_1 = 1, y_1 = 2, x_2 = 4, y_2 = 6\)
- \(d = \sqrt{(4 - 1)^2 + (6 - 2)^2}\)
- \(d = \sqrt{3^2 + 4^2}\)
- \(d = \sqrt{9 + 16}\)
- \(d = \sqrt{25}\)
- \(d = 5\)