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