Question

The distance $d$from $P_1=\left(x_1,y_1\right)$to $P_2=\left(x_2,y_2\right)$ is $d$ = _______ .

Short answer

The distance$d=\sqrt{{\left(x_2-x_1\right)}^2+{\left(y_2-y_1\right)}^2}$

Step-by-step solution

Step 1. Given information

We have been given two points $P_1=\left(x_1,y_1\right)$and $P_2=\left(x_2,y_2\right)$

We have to find the distance$d$between these two points.

Step 2. Find the distance between these two points.

Sketch these points on the coordinate axis.

The distance required between $P_1{P}_2$is $d$.

The distance between $P_1{P}_3$is $\left|x_2-x_1\right|$

The distance between $P_2{P}_3$is $\left|y_2-y_1\right|$

Using Pythagoras theorem,
role="math" localid="1646804280597" $$\begin{gathered} d^2={\left(x_2-x_1\right)}^2+{\left(y_2-y_1\right)}^2 \\ d=\sqrt{{\left(x_2-x_1\right)}^2+{\left(y_2-y_1\right)}^2} \end{gathered}$$