Chapter 21, Problem 1RE

To determine

Whether the statement” The distance between $\left(4,-3\right)$ and $\left(3,-4\right)$ is $\sqrt{2}$” is true or false.

Answer to Problem 1RE

The given statement is $\underset{\_}{\text{true}}$.

Explanation of Solution

Formula used:

The formula for distance between any two points $d=\sqrt{{\left(x_2-x_1\right)}^2-{\left(y_2-y_1\right)}^2}$.

Calculation:

Find the distance between two points $\left(x_1,y_1\right)=\left(4,-3\right)$ and $\left(x_2,y_2\right)=\left(3,-4\right)$.

$\begin{array}{c}d=\sqrt{{\left(4-3\right)}^2+{\left(-3-\left(-4\right)\right)}^2}\\ =\sqrt{1^2+{\left(-1\right)}^2}\\ =\sqrt{1+1}\\ =\sqrt{2}\end{array}$

Hence, the given statement is $\underset{\_}{\text{true}}$.