Question

Find the length of the line segment AB whose end points are A(2, −5) and B(−4, 7).

Answer 1

The given points are $A\left(2,-5\right)\text{and}B\left(-4,7\right)$.
Then, $\left(x_1=2,y_1=-5\right)\text{and}\left(x_2=-4,y_2=7\right)$
Therefore,
$$\begin{gathered} AB=\sqrt{{\left(x_2-x_1\right)}^2+{\left(y_2-y_1\right)}^2} \\ =\sqrt{{\left(-4-2\right)}^2+{\left(7+5\right)}^2} \\ =\sqrt{{\left(-6\right)}^2+{\left(12\right)}^2} \\ =\sqrt{36+144} \\ =\sqrt{180} \\ =6\sqrt{5}\text{units} \end{gathered}$$