find the distance between (1, -6) and (-5, -2)

Answer 1

To find the distance between the two points \((1, -6)\) and \((-5, -2)\), we can use the distance formula:

\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]

Here, \((x_1, y_1) = (1, -6)\) and \((x_2, y_2) = (-5, -2)\).

Now, let's calculate:

1. \(x_2 - x_1 = -5 - 1 = -6\)
2. \(y_2 - y_1 = -2 - (-6) = -2 + 6 = 4\)

Now plug these values into the distance formula:

\[ d = \sqrt{(-6)^2 + (4)^2} = \sqrt{36 + 16} = \sqrt{52} \]

We can simplify \(\sqrt{52}\):

\[ \sqrt{52} = \sqrt{4 \times 13} = \sqrt{4} \times \sqrt{13} = 2\sqrt{13} \]

Thus, the distance between the points \((1, -6)\) and \((-5, -2)\) is:

\[ \boxed{2\sqrt{13}} \]