Problem

Find the distance between the points A(2, -3) and B(5, 7).

Answer

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Answer

Finally, simplify to get the final answer: \(d = \sqrt{109}\).

Steps

Step 1 ：The distance between two points (x1, y1) and (x2, y2) is given by the distance formula \(d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\).

Step 2 ：Substitute the given points into the distance formula: \(d = \sqrt{(5 - 2)^2 + (7 - (-3))^2}\).

Step 3 ：Simplify the expression: \(d = \sqrt{3^2 + 10^2}\).

Step 4 ：Then, calculate the value: \(d = \sqrt{9 + 100}\).

Step 5 ：Finally, simplify to get the final answer: \(d = \sqrt{109}\).

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