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 (0,0), we can use the Distance Formula, which is given by \( d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \). For point A(5,6), the distance from the origin is \( d_A = \sqrt{(5 - 0)^2 + (6 - 0)^2} = \sqrt{25 + 36} = \sqrt{61} \). For point B(-2,5), the distance is \( d_B = \sqrt{(-2 - 0)^2 + (5 - 0)^2} = \sqrt{4 + 25} = \sqrt{29} \). Since \( \sqrt{29} < \sqrt{61} \), point B is closer to the origin. Now, let’s keep the fun going! Imagine the coordinates as participants in a race to the origin! Point A, with its vibrant coordinates, is like a sprinter who thinks they’re going to win but quickly finds out that Point B has a few tricks up its sleeve and crosses the finish line first with lesser distance. Next time you map out coordinates, think of them as quirky characters in a competitive journey!