What is the distance between the points \( (-2, -3) \) and \( (3, 5) \)?

To find the distance between the points \( (-2, -3) \) and \( (3, 5) \), you can use the distance formula, which is \( d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \). Here, \( (x_1, y_1) = (-2, -3) \) and \( (x_2, y_2) = (3, 5) \). So, \[ d = \sqrt{(3 - (-2))^2 + (5 - (-3))^2} = \sqrt{(3 + 2)^2 + (5 + 3)^2} = \sqrt{5^2 + 8^2} = \sqrt{25 + 64} = \sqrt{89}. \] Thus, the distance is \( \sqrt{89} \), which is approximately 9.43 units. Did you know that the distance formula is rooted in the Pythagorean theorem? That means every time you calculate a distance between two points in a plane, you're essentially using a geometric principle discovered well over 2,500 years ago! Pythagoras would certainly appreciate your math skills. It's also easy to stumble over the signs and order of the points! A common mistake is to forget which point is which when squaring the differences, leading to wrong calculations. Always double-check your subtraction for accuracy – it’s a simple slip that can throw off your final answer!