Distance Formula
The distance formula is a mathematical equation used to calculate the distance between two points in a coordinate plane
The distance formula is a mathematical equation used to calculate the distance between two points in a coordinate plane. It is often denoted as d = √((x2 – x1)^2 + (y2 – y1)^2), where (x1, y1) and (x2, y2) represent the coordinates of two points.
To understand how the distance formula works, let’s consider an example. Suppose we have two points on a coordinate plane: point A (2, 3) and point B (5, 7). We want to find the distance between these two points.
Step 1: Write down the coordinates of point A and point B:
– Point A: (x1, y1) = (2, 3)
– Point B: (x2, y2) = (5, 7)
Step 2: Apply the distance formula:
– d = √((x2 – x1)^2 + (y2 – y1)^2)
Plugging in the values:
– d = √((5 – 2)^2 + (7 – 3)^2)
Step 3: Simplify the equation:
– d = √(3^2 + 4^2)
– d = √(9 + 16)
– d = √25
– d = 5
Therefore, the distance between point A and point B is 5 units.
The distance formula can also be used in three-dimensional space by considering the additional z-coordinate. It follows the same concept but with an extra term for the z-coordinate, and the formula becomes d = √((x2 – x1)^2 + (y2 – y1)^2 + (z2 – z1)^2).
Remember, the distance formula is a useful tool when you need to find the distance between two points in a coordinate plane. It can be applied to various mathematical problems and is essential in geometry, physics, and other fields that deal with spatial relationships.
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