4) Find the distance between the points \( (8,-8) \) and \( (7,0) \). 4)) Write your answer as a whole number or a fully simplified radical expression. Do not (1)

To find the distance between the points \( (8,-8) \) and \( (7,0) \), you can use the distance formula, which is given by: \[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \] Plugging in your points where \( (x_1, y_1) = (8,-8) \) and \( (x_2, y_2) = (7,0) \): \[ d = \sqrt{(7 - 8)^2 + (0 - (-8))^2} \] \[ = \sqrt{(-1)^2 + (8)^2} \] \[ = \sqrt{1 + 64} \] \[ = \sqrt{65} \] So, the distance is \( \sqrt{65} \). Did you know that the concept of distance really took off in the 17th century with the advent of coordinate geometry, thanks to mathematicians like René Descartes? By merging algebra and geometry, they paved the way for all sorts of fun explorations like navigation, physics, and even computer graphics! In real-world scenarios, calculating distance is essential, whether you’re planning a road trip, designing a video game, or creating a flight path for a drone. Knowing how to accurately compute the distance between two points lets you optimize routes and understand spatial relationships, opening up a world of possibilities!