Answer :

Panoyin
[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]
iGreen
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]