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Sagot :
Recall that the distance formula is given by
[tex]d=\sqrt[]{\mleft({x_2-x_1}\mright)^2+\mleft({y_2-y_1}\mright)^2}[/tex]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)
[tex]\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}[/tex]Option A does not have a distance of 6 units, so it is not the correct option.
B. (1,8) (1,2)
[tex]\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}[/tex]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)
[tex]\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}[/tex]Option C does not have a distance of 6 units, so it is not the correct option.
D. (5,6) (5,5)
[tex]\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}[/tex]Option D does not have a distance of 6 units, so it is not the correct option.
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