A county wants to build one centrally$-$located processing facility to serve the county$$s four recycling drop$-$off locations. The four drop$-$offs have characteristics as given in the table below. What is the approximate center of gravity of these four locations?

Question $17$

A county wants to build one centrally$-$located processing facility to serve the county's four

recycling drop$-$off locations. The four drop$-$offs have characteristics as given in the table

below. What is the approximate center of gravity of these four locations?

Location X$-$coordinate Y$-$coordinate Tonnage

Drop$-$off point A $1$

$1$

$8,10$

Drop$-$off point B

$6$

$7$

$35$

Drop$-$off point C

$6$

$2$

$25$

Drop$-$off point $D$

$4$

$7$

$50$

$(x,Y)=(17,24)$

$(x,Y)=(6,4\mathrm{.}25)$

$(x,Y)=(4\mathrm{.}75,6\mathrm{.}04)$

$(x,Y)=(5\mathrm{.}25,6)$

Group of answer choices

$($X$,$ Y$)=(17,24)$

$($X$,$ Y$)=(6,4\mathrm{.}25)$

$($X$,$ Y$)=(4\mathrm{.}75,6\mathrm{.}04)$

$($X$,$ Y$)=(5\mathrm{.}25,6)$