Chapter 1.1, Problem 19AYU

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

37.

To determine

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

Answer to Problem 19AYU

$\sqrt{10}$

Explanation of Solution

Given:

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

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

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

$= \sqrt{{(-3)}^2+{(1)}^2}$

$= \sqrt{9+1}$

$= \sqrt{10}$

Therefore the distance is $= \sqrt{10}$