What is the distance between \( (4,2) \) and \( (8,5) \) ? Choose 1 answer: (A) 5 (B) 7 (C) \( \sqrt{12} \) (D) \( \sqrt{28} \)

To find the distance between the points \( (4,2) \) and \( (8,5) \), we can use the distance formula, which is \( d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \). Plugging in the values: \[ d = \sqrt{(8 - 4)^2 + (5 - 2)^2} = \sqrt{4^2 + 3^2} = \sqrt{16 + 9} = \sqrt{25} = 5 \] So the correct answer is (A) 5. To solidify this understanding, remember that the distance formula is derived from the Pythagorean theorem. You can visualize the two points as corners of a right triangle, where the distance between them forms the hypotenuse. It's a handy tool for many practical scenarios, from navigation to game design! Additionally, a common mistake when calculating distance is to forget to square the differences (the legs of the triangle) before summing them, which would lead you to an incorrect answer. So double-check your calculations!