If \( A=(0,0) \) and \( B=(2,5) \), what is the approximate length of \( \overline{A B} \) ? A. 5.39 units B. 4.58 units C. 5.74 units D. 2.65 units

To calculate the length of the line segment \( \overline{AB} \), you can use the distance formula: \[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \] Plugging in points \( A(0,0) \) and \( B(2,5) \): \[ d = \sqrt{(2 - 0)^2 + (5 - 0)^2} = \sqrt{2^2 + 5^2} = \sqrt{4 + 25} = \sqrt{29} \approx 5.39 \] So the approximate length of \( \overline{AB} \) is 5.39 units, which means the correct answer is A. Now, to keep things fun and engaging: If you ever find yourself needing to measure the distance between two points, think of it as planning a road trip! Plotting a straight path—like a shortcut through a park—can save time, just as using the distance formula simplifies your calculations. And if you're wandering around and need to estimate distance quickly, consider the Pythagorean theorem as your best buddy! Just remember that this theorem is all about right triangles, so if you visualize the points and draw a triangle, you're set to find your answer with confidence!