Question

How do you find the distance between the pair of points $\left( {6,2} \right)$ and $\left( {18,11} \right)$?

Answer 1

In the above question, we have to find the distance between these pair of points. Let us consider A with coordinates $\left( {6,2} \right)$ and B with $\left( {18,11} \right)$ . To find the distance between them AB applying the distance formula.

Complete step by step solution:
The distance between any two points in a plane is the line segment joining them. Consider two points A and B in the x-y plane. Let the coordinates of A be represented as $\left( {{x_1},{y_1}} \right)$ and coordinates of B be $\left( {{x_2},{y_2}} \right)$ . Applying distance formula to find the distance between them:
$AB = \sqrt {{{\left( {{x_2} - {x_1}} \right)}^2} + {{\left( {{y_2} - {y_1}} \right)}^2}}$
Now, coming back to the question we are given the coordinates of the points to be $\left( {6,2} \right)$ and $\left( {18,11} \right)$.
Applying the respective distance formula on these two points. Hence, the distance between them is
$\Rightarrow \sqrt {{{\left( {18 - 6} \right)}^2} + {{\left( {11 - 2} \right)}^2}} \\\ = \sqrt {{{\left( {12} \right)}^2} + {{\left( 9 \right)}^2}} \\\ = \sqrt {144 + 81} \\\ = \sqrt {225} \\\ = 15 \\\$
Therefore, the distance between the pair of points $\left( {6,2} \right)$ and $\left( {18,11} \right)$ is $15$.

Note: Distance between two points is always positive. Segments which have the same length are called congruent segments. Distance between two points in a three-dimensional space with coordinates $\left( {{x_1},{y_1},{z_1}} \right)$ and $\left( {{x_2},{y_2},{z_2}} \right)$ is represented as $\sqrt {{{\left( {{x_2} - {x_1}} \right)}^2} + {{\left( {{y_2} - {y_1}} \right)}^2} + {{\left( {{z_2} - {z_1}} \right)}^2}}$