Question

The distance between $(2,3)$ and $(-4,5)$ is _______

Answer 1

Determine the distance between $(2,3)$ and $(-4,5)$.

Given Coordinates:

$$\begin{gathered} (x_1,y_1)=(2,3) \\ (x_2,y_2)=(-4,5) \end{gathered}$$

Calculate the distance between two coordinates by using the formula:

$$\begin{gathered} \mathrm{D}=\sqrt{(x_2-x_1{)}^2+(y_2-y_1{)}^2} \\ \Rightarrow =\sqrt{(-4-2{)}^2+(5-3{)}^2} \\ \Rightarrow =\sqrt{(-6{)}^2+(2{)}^2} \\ \Rightarrow =\sqrt{36+4} \\ \Rightarrow =\sqrt{40} \\ \Rightarrow =2\sqrt{10}\because \surd 10=3.162 \\ \Rightarrow =2\times 3.162 \\ \Rightarrow =6.324 \end{gathered}$$

Hence, the distance between $(2,3)$ and $(-4,5)$ is $\underline{\mathbf{6}\mathbf{.}\mathbf{324}}$.