Calculating Distance Between Two Points Using the Distance Formula in a 2D Coordinate Plane

distance formula

The distance formula is a mathematical equation that calculates the distance between two points in a two-dimensional coordinate plane

The distance formula is a mathematical equation that calculates the distance between two points in a two-dimensional coordinate plane. The formula is derived from the Pythagorean theorem, which states that in a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

The distance formula is expressed as:

√((x2 – x1)^2 + (y2 – y1)^2)

Where:
– (x1, y1) represents the coordinates of the first point
– (x2, y2) represents the coordinates of the second point

To use the distance formula, follow these steps:

1. Identify the coordinates of the two points in the plane.
2. Substitute the x and y values of each point into the formula.
3. Calculate the differences between the x values and the y values.
4. Square the differences obtained in step 3.
5. Sum up the squared differences.
6. Take the square root of the sum obtained in step 5.
7. The resultant value is the distance between the two points.

Let’s use an example to illustrate the use of the distance formula. Suppose we have two points A(3, 4) and B(7, 8). To find the distance between these points, we can apply the distance formula:

Distance = √((7 – 3)^2 + (8 – 4)^2)
Distance = √(4^2 + 4^2)
Distance = √(16 + 16)
Distance = √32
Distance ≈ 5.66

Therefore, the distance between points A(3, 4) and B(7, 8) is approximately 5.66 units.

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