The length between the points (6,9) and (2,1)

To find the distance between the two points \((6, 9)\) and \((2, 1)\), we can use the distance formula:

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

Here, \((x_1, y_1) = (6, 9)\) and \((x_2, y_2) = (2, 1)\).

Now, substituting the values into the formula:

\[
d = \sqrt{(2 - 6)^2 + (1 - 9)^2}
\]
\[
d = \sqrt{(-4)^2 + (-8)^2}
\]
\[
d = \sqrt{16 + 64}
\]
\[
d = \sqrt{80}
\]
\[
d = \sqrt{16 \times 5} = 4\sqrt{5}
\]

Thus, the distance between the points \((6, 9)\) and \((2, 1)\) is \(4\sqrt{5}\).