Question

Length of the line segment joining the points $–1–\mathrm{i}$ and $2+3\mathrm{i}$ is

• A. $-5$
• B. $15$
• C. $5$
• D. $25$

Answer 1

The correct option is C

$5$

Explanation for correct option:

Calculating the distance between the given points:

Let two points given are:

$A(-1-\mathrm{\iota })$ and $B(2+3\mathrm{\iota })$.

Therefore,

$A(a_1,b_1)=\left(-1,-1\right)$ and

$B(a_2,b_2)=\left(2,3\right)$

Now the distance between $A$ and $B$ is given by:

$$\begin{gathered} AB=\sqrt{{\left(a_2-a_1\right)}^2+{\left(b_2-b_1\right)}^2} \\ =\sqrt{{\left(2-\left(-1\right)\right)}^2+{\left(3-\left(-1\right)\right)}^2} \\ =\sqrt{{\left(2+1\right)}^2+{\left(3+1\right)}^2} \\ =\sqrt{3^2+4^2} \\ =\sqrt{9+16} \\ =\sqrt{25} \\ AB=5 \end{gathered}$$

Therefore the distance between $A$ and $B$ is equal to $5$

Hence, the correct answer is option (C).