Answer :
[tex]d = \sqrt{(x_2 - x_1)^{2} + (y_2 - y_1)^{2}} \\d = \sqrt{(5 - 0)^{2} + (12 - 6)^{2}} \\d = \sqrt{(5)^{2} + (6)^{2}} \\d = \sqrt{25 + 36} \\d = \sqrt{61} \\d = 7.8 \\\\(x - h)^{2} + (y - k)^{2} = r^{2} \\(x - 5)^{2} + (y - 6)^{2} = 7.8^{2} \\(x - 5)^{2} + (y - 6)^{2} = 61 \\(h, k) = (5, 6)[/tex]
We can plug the two points into the distance formula.
[tex]\sf~d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
(0, 6), (5, 12)
x1 y1 x2 y2
Plug in what we know:
[tex]\sf~d=\sqrt{(5-0)^2+(12-6)^2}[/tex]
Subtract:
[tex]\sf~d=\sqrt{(5)^2+(6)^2}[/tex]
Simplify the exponents:
[tex]\sf~d=\sqrt{25+36}[/tex]
Add:
[tex]\sf~d=\sqrt{61}[/tex]
Simplify the square root:
[tex]\sf~d\approx\boxed{\sf7.81}[/tex]
[tex]\sf~d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
(0, 6), (5, 12)
x1 y1 x2 y2
Plug in what we know:
[tex]\sf~d=\sqrt{(5-0)^2+(12-6)^2}[/tex]
Subtract:
[tex]\sf~d=\sqrt{(5)^2+(6)^2}[/tex]
Simplify the exponents:
[tex]\sf~d=\sqrt{25+36}[/tex]
Add:
[tex]\sf~d=\sqrt{61}[/tex]
Simplify the square root:
[tex]\sf~d\approx\boxed{\sf7.81}[/tex]