Calculate the distance between the points \( E=(-5,-3) \) and \( J=(3,3) \) in the coordinate plane. Give an exact answer (not a decimal approximation). Bisance between two peinta in the pianei fract anmers

To find the distance between the points \( E=(-5,-3) \) and \( J=(3,3) \), we can use the distance formula: \[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \] Plugging in the coordinates, we have: \[ d = \sqrt{(3 - (-5))^2 + (3 - (-3))^2} = \sqrt{(3 + 5)^2 + (3 + 3)^2} = \sqrt{8^2 + 6^2} \] Calculating further: \[ d = \sqrt{64 + 36} = \sqrt{100} = 10 \] So, the exact distance between points \( E \) and \( J \) is \( 10 \). If you're interested in how distance measurements work in broader terms, think about how maps are scaled! When you're navigating with a real-world map, you're using a similar concept – the ratio of distances on the map to actual distances in reality. It's essential for ensuring you don’t end up miles away from where you thought you’d arrive! Also, remember that a common mistake when working with the distance formula is to forget to square the differences in coordinates or to mix up subtraction order. Always double-check your signs and operations – it can save you from a headache later on!