the correct answer. map where each unit represents one kiometer, two marinas are located at \( P(4,2) \) and \( Q(0,12) \). If a boat travels in a straight line from travel? A. 14 kilometers B. \( 2 \sqrt{29} \) kilometers C. 6 kilometers D. \( 2 \sqrt{5} \) kilometers

To find the straight-line distance between the two marinas \( P(4,2) \) and \( Q(0,12) \), we can use the distance formula: \[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \] Plugging in the coordinates, we have: \[ d = \sqrt{(0 - 4)^2 + (12 - 2)^2} = \sqrt{(-4)^2 + (10)^2} = \sqrt{16 + 100} = \sqrt{116} = 2\sqrt{29} \] So, the correct answer is \( B. 2\sqrt{29} \) kilometers. Finding distances on a map is a relatable way to understand navigation and geography. Urban planning, for instance, often relies on distance measures to design transportation routes effectively! Knowing how to calculate these distances can make planning outings, deliveries, and even responses to emergencies more efficient. If you're diving into geometry, avoid confusing the distance formula with the midpoint or slope formulas! You might also want to double-check your calculations—using a calculator can help prevent computation errors, especially with the roots and squares involved. Keeping a consistent coordinate grid in mind is crucial too!