A chain of home health care firms in Louisiana needs to locate a central office from which to conduct internal audits and other periodic reviews of its facilities. These facilities are scattered throughout the$$ state, as detailed in the following table. Each$$ site, except for$$ Houma, will be visited three times each year by a team of$$ workers, who will drive from the central office to the site. Houma will be visited five times a year.

$$

Map Coordinates

City

X

Y

Covington

$9\mathrm{.}0$

$3\mathrm{.}5$

Donaldsonville

$7\mathrm{.}5$

$2\mathrm{.}8$

Houma

$7\mathrm{.}6$

$1\mathrm{.}4$

Monroe

$5\mathrm{.}2$

$8\mathrm{.}7$

Natchitoches

$2\mathrm{.}6$

$6\mathrm{.}8$

New Iberia

$5\mathrm{.}3$

$2\mathrm{.}4$

Opelousas

$5\mathrm{.}2$

$3\mathrm{.}3$

Ruston

$3\mathrm{.}8$

$8\mathrm{.}5$

For the location of the new central$$ office, the coordinates should be$$ near:

Part $2$

x$=$ enter your response here $($round your response to two decimal$$ places$).$