Question

What is the distance between the $A\left(4,-2\right)\text{and}\left(-4,-8\right)$.

localid="1648622424791" $\begin{array}{l}\left(A\right)6\left(B\right)8\\ \left(C\right)10\left(D\right)14\end{array}$

Short answer

The distance between the given pair of points is $10\text{units}$. Hence option (C) is correct.

Step-by-step solution

Step 1. Write down the given information.

The given pair of points have coordinates $A\left(4,-2\right)\text{and}\left(-4,-8\right)$.

Step 2. Concept used.

If a line segment has end-points at$\left(x_1,y_1\right)\text{and}\left(x_2,y_2\right)$ then the distance $\left(d\right)$between these points is given as:

Step 3. Calculation.

The distance $\left(d\right)$between the pair of points with given coordinates$A\left(4,-2\right)\text{and}\left(-4,-8\right)$is evaluated using the formula (1) stated above.

$\begin{array}{c}\left|d\right|=\sqrt{{\left(x_2-x_1\right)}^2+{\left(y_2-y_1\right)}^2}\\ =\sqrt{{\left(-4-4\right)}^2+{\left(-8+2\right)}^2}\\ =\sqrt{{\left(-8\right)}^2+{\left(-6\right)}^2}\\ =10\text{units}\end{array}$

Step 4. Conclusion.

The distance between the given pair of points is $10\text{units}$. So, option (C) is correct.