Let
A--------> the coordinates in a Cartesian Plane of Frostburg Mall
B--------> the coordinates in a Cartesian Plane of Sojourner Truth Park
C--------> the coordinates in a Cartesian Plane of City Center (0,0)
Step [tex] 1 [/tex]
Find the coordinates of Frostburg Mall (point A)
we know that
The mall is [tex] 3 [/tex] miles west and [tex] 2 [/tex] miles south of the City Center
so
[tex] x\ coordinate=0-3\\ x\ coordinate=-3 [/tex]
[tex] y\ coordinate=0-2\\ x\ coordinate=-2 [/tex]
Point A is equal to [tex] (-3,-2) [/tex]
Step [tex] 2 [/tex]
Find the coordinates of Sojourner Truth Park (point B)
we know that
The park is [tex] 4 [/tex] miles east and [tex] 5 [/tex] miles north of the City Center
so
[tex] x\ coordinate=0+4\\ x\ coordinate=4 [/tex]
[tex] y\ coordinate=0+5\\ x\ coordinate=5 [/tex]
Point B is equal to [tex] (4,5) [/tex]
Step [tex] 3 [/tex]
Find the distance point A and point B
[tex] A (-3,-2)\ B (4,5) [/tex]
we know that the distance formula is equal to
[tex] d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}} [/tex]
[tex] dAB=\sqrt{(5+2)^{2}+(4+3)^{2}} [/tex]
[tex] dAB=\sqrt{(7)^{2}+(7)^{2}} [/tex]
[tex] dAB=\sqrt{98}} \\ dAB=9.9\ miles [/tex]
therefore
the answer is
The distance from the mall to the park is [tex] 9.9\ miles [/tex]
