Find the exact distance between the points. \[ (-9,4) \text { and }(-5,-6) \] Select one: a. $10 \sqrt{2}$ b. $2 \sqrt{29}$ C. 200 d. 116

Step 1 ：We are given two points (-9,4) and (-5,-6) and we are asked to find the exact distance between these points.

Step 2 ：The distance between two points in a 2D plane can be calculated using the distance formula derived from the Pythagorean theorem. The distance between points (x1, y1) and (x2, y2) is given by: \(\sqrt{(x2 - x1)^2 + (y2 - y1)^2}\)

Step 3 ：Substitute the given points into the formula to find the distance: \(\sqrt{(-5 - (-9))^2 + (-6 - 4)^2}\)

Step 4 ：Simplify the expression inside the square root: \(\sqrt{(4)^2 + (-10)^2}\)

Step 5 ：Calculate the squares: \(\sqrt{16 + 100}\)

Step 6 ：Add the numbers inside the square root: \(\sqrt{116}\)

Step 7 ：Calculate the square root: 10.770329614269007

Step 8 ：The calculated distance does not exactly match any of the given options. However, it is closest to option b. \(2 \sqrt{29}\), which is approximately 10.770329614269007.

Step 9 ：Therefore, the correct answer is option b. \(2 \sqrt{29}\)

Step 10 ：Final Answer: \(\boxed{2 \sqrt{29}}\)