Answer:
10.8 units.
Step-by-step explanation:
Given:
Centers of two circles are [tex](5,-4)[/tex] and [tex](-4,2)[/tex].
Distance between two points [tex](x_{1},y_{1})[/tex] and [tex](x_{2},y_{2})[/tex] is given as:
Distance, [tex]D=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}[/tex]
Here, [tex](x_{1},y_{1})[/tex] is [tex](5,-4)[/tex] and [tex](x_{2},y_{2})[/tex] is [tex](-4,2)[/tex].
Plug in these values and calculate the distance between these 2 points.
Distance between the centers is given as:
[tex]D=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}\\ D=\sqrt{(-4-5)^{2}+(2-(-4))^{2}}\\ D=\sqrt{(-9)^{2}+(6)^{2}}\\ D=\sqrt{81+36}\\ D=\sqrt{117}=10.8[/tex]
Therefore, the distance between the centers of the two circles is 10.8 units.
