When students use the distance and midpoint formulas, they can make some common mistakes that might make it hard for them to really understand coordinate geometry. Here are some of these mistakes to watch out for:

1. Not Understanding the Formulas:

   • The distance formula looks like this:
     $d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$
     And the midpoint formula is:
     $M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)$
     Many students memorize these formulas but don’t really understand what they mean. This can be confusing when they have to use the formulas in different problems or see them in various ways.

2. Incorrectly Identifying Points:

   • Another mistake happens when students don’t correctly identify the coordinates of the points.
     It is very important to carefully look at the points you are working with. Making a mistake here can lead to the wrong answer.

By keeping these tips in mind, students can improve their skills in applying these important formulas.