Answer:
12. a
13a. (-3, 2)
13b.[tex]12\sqrt{2}[/tex]
13c. [tex]( x +3 )^2 + ( y - 2 )^2 = 288[/tex]
Step-by-step explanation:
13a. Graph endpoints and find the center, and to find the center we can use the midpoint formula.
[tex]midpoint = (\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})\\ = (\frac{-9+3}{2},\frac{-4+8}{2})\\= (\frac{-6}{2},\frac{4}{2})\\ = (-3,2)[/tex]
13b. Use given points and use distance formula to find radius.
[tex]distance = \sqrt{({x_2-x_1})^2+({y_2-y_1})^2}\\= \sqrt{({3-(-9)})^2+({8-(-4)})^2}\\= \sqrt{({3+9})^2+({8+4})^2}\\=\sqrt{({12})^2+({12})^2}\\ =\sqrt{({12})^2+({12})^2}\\= \sqrt{144+144} = \sqrt{288} = 12\sqrt{2}[/tex]
13c. Refer back to 13a and 13b to setup the equation of the circle.
[tex]( x - h )^2 + ( y - k )^2 = r^2\\( x - (-3) )^2 + ( y - 2 )^2 = (12\sqrt{2})^2\\( x +3 )^2 + ( y - 2 )^2 = 288[/tex]
Sorry if it looks long but I hope that helps!
