Find the distance between the pair of points. \( (2,6) \) and \( (-4,5) \)

To find the distance between the points \( (2,6) \) and \( (-4,5) \), you can use the distance formula: \[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \] Plugging the points into the formula where \( (x_1, y_1) = (2, 6) \) and \( (x_2, y_2) = (-4, 5) \), we have: \[ d = \sqrt{((-4) - 2)^2 + (5 - 6)^2} \] \[ d = \sqrt{(-6)^2 + (-1)^2} \] \[ d = \sqrt{36 + 1} \] \[ d = \sqrt{37} \] So the distance between the points \( (2,6) \) and \( (-4,5) \) is \( \sqrt{37} \). A fun fact: This formula is a crucial tool in geometry. It not only helps to find the distance in a 2D plane, but can also be extended for 3D spaces. Moreover, in real-life scenarios, you might use this distance calculation in navigation applications. Whether you’re plotting a route on a map or figuring out how far apart two locations are for a delivery, understanding this simple yet powerful formula is essential!