Given the following coordinates of A and B below,
[tex]\begin{gathered} A(x_1,y_1)=(-6,4) \\ B(x_2,y_2)=(3,4) \end{gathered}[/tex]To find the distance between coordinates A and B, the formula is,
[tex]d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]Substituting the points into the formula given above,
[tex]\begin{gathered} d=\sqrt[]{(3-(-6)^2+(4-4)^2} \\ d=\sqrt[]{9^2+0^2}=\sqrt[]{81+0}=\sqrt[]{81}=9\text{ units} \end{gathered}[/tex]Since the distance between the two points is 9 units,
[tex]\begin{gathered} \lvert-6\rvert\text{ is 6 because the absolute value of a number is always positive} \\ \lvert3\rvert\text{ is} \\ \lvert-6\rvert+\lvert3\rvert=9\text{ units} \end{gathered}[/tex]Hence, A is the right option.
