Chapter 1.1, Problem 38AYU

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

40. $P_1=\left(-1,\text{ 0}\right);P_2=\left(2,4\right)$

To determine

To calculate: The distance $\text{d(P}₁\text{, P}₂\text{)}$ between the points $\text{P}₁\left(\text{-1, 0}\right)$ and $\text{P}₂\left(\text{2, 4}\right)$.

Answer to Problem 38AYU

5

Explanation of Solution

Given:

The points $\text{P}₁\text{= (x}₁\text{, y}₁\text{) = }\left(-1,0\right)$ and $\text{P}₂\text{= (x}₂\text{, y}₂\text{) = }\left(2,4\right)$.

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

$= \sqrt{{(2-\left(-1\right))}^2+{(4-0)}^2}$

$= \sqrt{{(2+1)}^2+{(4)}^2}$

$= \sqrt{{(3)}^2+{(4)}^2}$

$= \sqrt{9+16}$

$= \sqrt{25}$

$= 5$

Therefore the distance is $= 5$