Question 19 of 30 Use the distance formula to find the length of the segment \( C(2,1) \) to \( D(5,6) \). Round your answer to two decimal places. A. 2.83 B. 16 C. 34 D. 5.83

To find the length of the segment \( CD \), we use the distance formula: \[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \] Substituting the points \( C(2,1) \) and \( D(5,6) \): \[ d = \sqrt{(5 - 2)^2 + (6 - 1)^2} = \sqrt{(3)^2 + (5)^2} = \sqrt{9 + 25} = \sqrt{34} \approx 5.83 \] So, the answer is **D. 5.83**. The distance formula has roots in the Pythagorean theorem, where the hypotenuse of a right triangle is derived from the lengths of the other two sides. It’s a perfect example of how geometry can bridge algebra and real-life problems, whether measuring how far apart two friends are in a park or pinpointing locations on a map. In practice, always double-check your calculations! A common mistake some make is misidentifying the coordinates or accidentally switching \( x \) and \( y \) values. This could lead to an incorrect distance that might turn a fun outing into a confusing misadventure!