Question

Find the distance between the points given. (0,6) and (5,12)

Answer 1

We can plug the two points into the distance formula.

$\sf~d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

(0, 6), (5, 12)
x1 y1 x2  y2

Plug in what we know:

$\sf~d=\sqrt{(5-0)^2+(12-6)^2}$

Subtract:

$\sf~d=\sqrt{(5)^2+(6)^2}$

Simplify the exponents:

$\sf~d=\sqrt{25+36}$

Add:

$\sf~d=\sqrt{61}$

Simplify the square root:

$\sf~d\approx\boxed{\sf7.81}$

Answer 2

$d = \sqrt{(x_2 - x_1)^{2} + (y_2 - y_1)^{2}} \\d = \sqrt{(5 - 0)^{2} + (12 - 6)^{2}} \\d = \sqrt{(5)^{2} + (6)^{2}} \\d = \sqrt{25 + 36} \\d = \sqrt{61} \\d = 7.8 \\\\(x - h)^{2} + (y - k)^{2} = r^{2} \\(x - 5)^{2} + (y - 6)^{2} = 7.8^{2} \\(x - 5)^{2} + (y - 6)^{2} = 61 \\(h, k) = (5, 6)$