Question

The distance between the points $(0,5)$ and $(-5,0)$ is

• A. $5$
• B. $5\sqrt{2}$
• C. $2\sqrt{5}$
• D. $10$

Answer 1

The correct option is B

$5\sqrt{2}$

Determine the distance between the points $(0,5)$ and $(-5,0)$.

Explanation for Correct answer:

The explanation for the correct option:

Point:

$$\begin{gathered} (x_1,y_1)=(0,5) \\ (x_2,y_2)=(-5,0) \end{gathered}$$

Use the distance formula to calculate the distance:

$$\begin{gathered} \mathrm{Distance}\left(D\right)=\sqrt{{(x_2-x_1)}^2+{(y_2-y_1)}^2} \\ =\sqrt{{(-5-0)}^2+{(0-5)}^2} \\ =\sqrt{{(-5)}^2+{(-5)}^2} \\ =\sqrt{25+25} \\ =\sqrt{50} \\ =5\sqrt{2} \end{gathered}$$

Hence, the distance between the points $(0,5)$ and $(-5,0)$ is $\mathbf{5}\sqrt{\mathbf{2}}$, that is equivalent to "Option B".

The explanation for the incorrect option:

Since the distance between the point is $\mathbf{5}\sqrt{\mathbf{2}}$ is calculated above is not equivalent to the values mentioned in Option A, Option C, and Option D.
Hence, Option A, Option C, and Option D. are incorrect options.

Hence, the correct option is Option B.