Find the distance between the two points. Simplify your answer, and write the exact answer in simplest radical form for irrational answers. $(x, y)=(-3,2)$ and $(x, y)=(1,-7)$

Step 1 ：Given two points in a plane, $(x_1, y_1) = (-3, 2)$ and $(x_2, y_2) = (1, -7)$.

Step 2 ：The distance between these two points can be calculated using the distance formula derived from the Pythagorean theorem: \(\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\).

Step 3 ：Substitute the given values into the formula to find the distance: \(\sqrt{(1 - (-3))^2 + (-7 - 2)^2}\).

Step 4 ：Simplify the expression inside the square root: \(\sqrt{(4)^2 + (-9)^2}\).

Step 5 ：Further simplify the expression: \(\sqrt{16 + 81}\).

Step 6 ：Add the numbers inside the square root: \(\sqrt{97}\).

Step 7 ：The distance calculated is a decimal number. However, the question asks for the exact answer in simplest radical form for irrational answers. This means we need to convert the decimal number to a radical form.

Step 8 ：The decimal number is approximately equal to \(\sqrt{97}\), which is an irrational number in simplest radical form.

Step 9 ：Final Answer: The distance between the two points is \(\boxed{\sqrt{97}}\).