Respuesta :
We are given two points in a cartesian coordinate system as follows:
[tex]A\text{ ( 9 , 3 ) ; B ( -3 , 3 )}[/tex]We are to determine the distance between points A and B.
The distance formula for cartesian coordinate plane is given as:
[tex]|AB|=\sqrt{(x_2-x_1)^2+\left(y_2-y_1\right)^2}[/tex]Where,
[tex]\begin{gathered} A\colon(x_1,y_1)\text{ = ( 9 , 3 )} \\ B\colon(x_2,y_2)\text{ = ( -3 , 3 )} \end{gathered}[/tex]We will go ahead an plug the respective coordinates in the distance formula for AB as follows:
[tex]\begin{gathered} |AB|=\sqrt{(-3-9)^2+\left(3-3\right)^2} \\ |AB|=\sqrt{(-12)^2+\left(0\right)}\text{ = }\sqrt{12^2} \\ |AB|=\text{ 12 units} \end{gathered}[/tex]Since, the distance between points A and B is an integer; hence, the answer to nearest hundredth would be:
[tex]\textcolor{#FF7968}{|AB|=12}\text{\textcolor{#FF7968}{ units}}[/tex]