Question

Which points are separated by a distance of 6 units? O A. (2, 4) (2, 2) B. (1,8) (1,2) c. (3, 1) (3,6) D. (5,6) (5,5)

Answer 1

Recall that the distance formula is given by

$d=\sqrt[]{\mleft({x_2-x_1}\mright)^2+\mleft({y_2-y_1}\mright)^2}$

We are asked to find out which of the given points have a distance of 6 units?

Let us analyze each option.

A. (2, 4) (2, 2)

$\begin{gathered} d=\sqrt[]{({x_2-x_1})^2+({y_2-y_1})^2} \\ d=\sqrt[]{({2-2_{}})^2+({2-4})^2} \\ d=\sqrt[]{({0})^2+({-2})^2} \\ d=\sqrt[]{4}^{} \\ d=2 \end{gathered}$

Option A does not have a distance of 6 units, so it is not the correct option.

B. (1,8) (1,2)

$\begin{gathered} d=\sqrt[]{({x_2-x_1})^2+({y_2-y_1})^2} \\ d=\sqrt[]{({1-1})^2+({2-8})^2} \\ d=\sqrt[]{({0})^2+({-6})^2} \\ d=\sqrt[]{36}^{} \\ d=6 \end{gathered}$

As you can see, the distance between these points is exactly 6 units.

Therefore, Option B is the correct answer.

c. (3, 1) (3,6)

$\begin{gathered} d=\sqrt[]{({x_2-x_1})^2+({y_2-y_1})^2} \\ d=\sqrt[]{({3-3})^2+({6-1})^2} \\ d=\sqrt[]{(0)^2+({5})^2} \\ d=\sqrt[]{25} \\ d=5 \end{gathered}$

Option C does not have a distance of 6 units, so it is not the correct option.

D. (5,6) (5,5)​

$\begin{gathered} d=\sqrt[]{({x_2-x_1})^2+({y_2-y_1})^2} \\ d=\sqrt[]{({5-5})^2+({5-6})^2} \\ d=\sqrt[]{({0})^2+({-1})^2} \\ d=\sqrt[]{1}^{} \\ d=1 \end{gathered}$

Option D does not have a distance of 6 units, so it is not the correct option.