Q. 43 - Precalculus Enhanced with Graphing Utilities

Question

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

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

Step-by-Step Solution

Answer

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

Step 1. Given information.

Find the distance between the points.

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

Step 2. Substitute the values in the formula.

The length of the line segment is the distance between the points $P_1=(x_1,y_1)=(a,b) \mathrm{and} P_2=(x_2,y_2)=(0,0)$. Using the distance formula with $x_1=a, y_1=b, x_2=0, \mathrm{and} y_2=0$the length d is

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

Step 3. Conclusion.

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