Question

Find the distance $d(P_1,P_2)$between the points $P_1\mathrm{and}{P}_2$.

$P_1=(a,a);P_2=(0,0)$

Short answer

The distance between the points is$d=a\sqrt{2}$.

Step-by-step solution

Step 1. Given information.

Find the distance between the points.

$P_1=(a,a);P_2=(0,0)$

Step 2. Substitute the values in the formula.

The length of the line segment is the distance between the points $P_1=(x_1,y_1)=(a,a)\mathrm{and}{P}_2=(x_2,y_2)=(0,0)$.Using the distance formula with $x_1=a,y_1=-a,x_2=0,\mathrm{and}{y}_2=0$, the length d is

$$\begin{gathered} d=\sqrt{{\left(x_2-x_1\right)}^2+{(y_2-y_2)}^2} \\ d=\sqrt{{\left(0-a\right)}^2+{(0-a)}^2} \\ d=\sqrt{a^2+a^2} \\ d=\sqrt{2a^2} \\ d=a\sqrt{2} \end{gathered}$$

Step 3. Conclusion. 

The distance between the points is$a\sqrt{2}$.