The coordinates of Bumper cars is :
[tex](-4,-3)[/tex]
Coordinates of Entrance is (-8,0) and coordinates of darts is (1 , -6)
To find whether the Bumpers cars is closer to entrance or darts:
The distance can be given by the distance formula:
If A(x1,y1) and B(x2,y2) are the points then the distance formula is given by:
[tex]AB=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Hence, the distance between bumper cars and entrance is given by:
[tex]\begin{gathered} BE=\sqrt[]{(-8-(-4))^2+(0-(-3))^2} \\ =\sqrt[]{(-8+4)^2+(3^2)} \\ =\sqrt[]{(-4)^2+9} \\ =\sqrt[]{16+9} \\ =\sqrt[]{25} \\ =5 \end{gathered}[/tex]
Similarly, distance between darts and bumper cars is given by:
[tex]\begin{gathered} BD=\sqrt[]{(1-(-4))^2+(-6-(-3))^2} \\ =\sqrt[]{(1+4)^2+(-6+3)^2} \\ =\sqrt[]{5^2+(-3)^2} \\ =\sqrt[]{25+9} \\ =\sqrt[]{34} \\ =5.83095\text{ } \end{gathered}[/tex]
Since, the distance between bumper cars and the darts is greater than the distance between bumper cars and entrance, hence bumper cars is closer to entrance.
