Question

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

Answer 1

`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 = √(25 + 36) \\d = √(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)`

Answer 2

We can plug the two points into the distance formula.


`\sf~d=√((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=√((5-0)^2+(12-6)^2)`

Subtract:


`\sf~d=√((5)^2+(6)^2)`

Simplify the exponents:


`\sf~d=√(25+36)`

Add:


`\sf~d=√(61)`

Simplify the square root:


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