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

To find the distance between the points \( (-2, -3) \) and \( (3, 5) \), we can use the distance formula, which is given by: \[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \] Here, \( (x_1, y_1) = (-2, -3) \) and \( (x_2, y_2) = (3, 5) \). First, calculate \( x_2 - x_1 \) and \( y_2 - y_1 \): - \( x_2 - x_1 = 3 - (-2) = 3 + 2 = 5 \) - \( y_2 - y_1 = 5 - (-3) = 5 + 3 = 8 \) Now plug these values into the distance formula: \[ d = \sqrt{(5)^2 + (8)^2} = \sqrt{25 + 64} = \sqrt{89} \] Thus, the distance between the points \( (-2, -3) \) and \( (3, 5) \) is \( \sqrt{89} \), which is approximately 9.43 units. When calculating distances, it's good to remember that coordinate geometry sometimes springs surprises! If you have a coordinate grid handy, try plotting your points—seeing those two locations can really solidify your understanding of distance! If you're ever unsure about your calculations, don’t forget the power of checking your work! Mistakes often happen during squaring or simplifying, so it’s handy to double-check each step along the way. Grab a calculator, or better yet, graphing software—you’ll be flying through geometry in no time!