Find the distance between the two points. Simplify your answer, and write the exact answer in simplest radical form for irrational answers.
$(x, y) = (- 8, 3) and (x, y) = (3, - 9)$

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Final Answer: The distance between the two points is $\sqrt{265}$

Steps

Step 1 ：Given two points in a 2D plane, (-8, 3) and (3, -9), we are asked to find the distance between these points.

Step 2 ：The distance between two points (x1, y1) and (x2, y2) can be calculated using the distance formula derived from the Pythagorean theorem: $d = \sqrt{(x 2 - x 1)^{2} + (y 2 - y 1)^{2}}$

Step 3 ：Substitute the given points into the formula: $d = \sqrt{(3 - (- 8))^{2} + ((- 9) - 3)^{2}}$

Step 4 ：Simplify the expression inside the square root: $d = \sqrt{(11)^{2} + (- 12)^{2}}$

Step 5 ：Calculate the squares: $d = \sqrt{121 + 144}$

Step 6 ：Add the results: $d = \sqrt{265}$

Step 7 ：Final Answer: The distance between the two points is $\sqrt{265}$

Find the distance between the two points. Simplify your answer, and write the exact answer in simplest radical form for irrational answers.(x,y)=(−8,3) and (x,y)=(3,−9)

Answer

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Find the distance between the two points. Simplify your answer, and write the exact answer in simplest radical form for irrational answers.
$(x, y) = (- 8, 3) and (x, y) = (3, - 9)$