Question

The distance between the points A(0, 5) and B(−5, 0) is

(a) 5 units
(b) $2\sqrt{5}$ units
(c) $\sqrt{10}$ units
(d) $5\sqrt{2}$ units

Answer 1

(d) $5\sqrt{2}$ units
The given points are A(0, 5) and B(−5, 0).
Then, $\left(x_1=0,y_1=5\right)\text{and}\left(x_2=-5,y_2=0\right)$
Therefore,
$$\begin{gathered} AB=\sqrt{{\left(x_2-x_1\right)}^2+{\left(y_2-y_1\right)}^2} \\ =\sqrt{{\left(-5-0\right)}^2+{\left(0-5\right)}^2} \\ =\sqrt{{\left(-5\right)}^2+{\left(-5\right)}^2} \\ =\sqrt{25+25} \\ =\sqrt{50} \\ =5\sqrt{2}\text{units} \end{gathered}$$