In this exercise we use the Distance Formula, Which of the points \( A(5,6) \) or \( B(-2,5) \) is closer to the origin? Point \( A \) is closer to the origin. Point \( B \) is closer to the origin. Points \( A \) and \( B \) are the same distance from the origin.

To determine which point is closer to the origin, we can use the Distance Formula: \( d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \). For point A, the distance to the origin (0,0) is \( d_A = \sqrt{(5-0)^2 + (6-0)^2} = \sqrt{5^2 + 6^2} = \sqrt{25 + 36} = \sqrt{61} \). For point B, the distance is \( d_B = \sqrt{(-2-0)^2 + (5-0)^2} = \sqrt{(-2)^2 + 5^2} = \sqrt{4 + 25} = \sqrt{29} \). Since \( \sqrt{29} < \sqrt{61} \), point B is closer to the origin. In real-world terms, knowing how to apply the Distance Formula not only helps in geometry but also in fields like navigation and mapping. For example, if you're plotting a route on a map or trying to find the shortest pathway from point A to point B, this formula comes in handy! Plus, if you ever need to calculate airplane distances or even phone tower ranges, you’ll rely on this fundamental principle of geometry.