Question

How do I find the distance between two points?

Answer 1

Hint:
In the given question, we have been asked to calculate the distance between two arbitrary points. When we have to calculate the distance between any two points, we use a single formula, which is the distance formula. This formula calculates the distance between any two given points in the two-dimensional plane, or in the \[xy\] plane.

Complete step by step answer:
Let the two given points be \[A,B\] with coordinates \[\left( {{x_1},{y_1}} \right),\left( {{x_2},{y_2}} \right)\] respectively.
Now, if we want to calculate the distance between the points \[A\] and \[B\], then we can do so by using the Euclidean distance formula, with which we get,
Distance between \[A\] and \[B\], \[\left| {AB} \right| = \sqrt {{{\left( {{x_2} - {x_1}} \right)}^2} + {{\left( {{y_2} - {y_1}} \right)}^2}} \]

Additional Information:
The distance formula for the distance between any two given points with coordinates \[\left( {{x_1},{y_1}} \right),\left( {{x_2},{y_2}} \right)\] in the \[xy\] plane or the two-dimensional plane is represented as:
\[d = \sqrt {{{\left( {{x_2} - {x_1}} \right)}^2} + {{\left( {{y_2} - {y_1}} \right)}^2}} \]
The distance formula for the distance between any two given points with coordinates \[\left( {{x_1},{y_1},{z_1}} \right),\left( {{x_2},{y_2},{z_2}} \right)\] in the \[xyz\] plane or the three-dimensional plane is represented as:
\[d = \sqrt {{{\left( {{x_2} - {x_1}} \right)}^2} + {{\left( {{y_2} - {y_1}} \right)}^2} + {{\left( {{z_2} - {z_1}} \right)}^2}} \]

Note:
In this question, we had to write the formula for the distance between any two given points. This was assuming the fact that the two points lie in the \[xy\] plane. This \[xy\] plane is more commonly known as the two-dimensional plane. This formula can be used to calculate the distance between any two points in any of the four quadrants.