5. Find the distance between \( P(2,8) \) and \( Q(5,3) \) 9 34 \( \sqrt{18} \) \( \sqrt{34} \)

To find the distance between the points \( P(2,8) \) and \( Q(5,3) \), you can use the distance formula: \[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \] Substituting the coordinates: \[ d = \sqrt{(5 - 2)^2 + (3 - 8)^2} = \sqrt{3^2 + (-5)^2} = \sqrt{9 + 25} = \sqrt{34}. \] So, the correct distance is \( \sqrt{34} \). Knowing how to apply the distance formula can help you in various situations, such as in geometry, physics, and even navigation. The formula is quite handy for calculating distances in any 2D space, especially when mapping out coordinates or even checking the straight-line distance between two locations on a map! A common mistake when using this formula is forgetting to square the differences. Remember, each difference \((x_2 - x_1)\) and \((y_2 - y_1)\) needs to be squared before you add them together. Skipping this step might lead you to an incorrect distance, so always double-check your arithmetic!