Chapter 1.1, Problem 18AYU

In Problems 35-46, find the distance $d\left(P_1,P_2\right)$ between the points $P_1$ and $P_2$.

36.

To determine

To calculate: The distance $\text{d(P}₁\text{, P}₂\text{)}$ between the points $\text{P}₁\left(\text{0, 0}\right)$ and $\text{P}₂\left(-2,1\right)$

Answer to Problem 18AYU

$\sqrt{5}$

Explanation of Solution

Given:

The points $\text{P}₁\text{= (x}₁\text{, y}₁\text{) = }\left(\text{0, 0}\right)$ and $\text{P}₂\text{= (x}₂\text{, y}₂\text{) = }\left(-2,1\right)$

Formula used:

Distance formula:

$\text{d(P}₁\text{,P}₂\text{) =}$ $\sqrt{{(x_2-x_1)}^2+{(y_2-y_1)}^2}$

Calculation:

Distance $\text{P}₁\text{P}₂=\sqrt{{(x_2-x_1)}^2+{(y_2-y_1)}^2}$

$= \sqrt{{(-2-0)}^2+{(1-0)}^2}$

$= \sqrt{{(-2)}^2+{(1)}^2}$

$= \sqrt{4+1}$

$= \sqrt{5}$

Therefore the distance is $= \sqrt{5}$