Distance Between Two Points, Exact Answers

Start with the grid sheets so students see the right triangle, then move to exact answers from coordinates. Use the error analysis sheet to check understanding.

Find ten distances like (1, 2) to (4, 6) from coordinate differences, as whole numbers or square roots. The directions on the page read: Find the distance d between each pair of points. Find the legs a and b from the coordinates, then use a² + b² = c². Write d as a whole number or a square root. An answer key is included.

Yes, both. We made it for 8th grade Pythagorean theorem, and it works the same at home or at school. At home, a student can work through it alone and then go over it with you, which shows quickly what is solid and what needs another look. In class it works as independent practice, homework or a warm-up, and you can print one copy or a full set.

Subtract the x coordinates and the y coordinates to get the two legs, then use a² + b² = c². From (1, 2) to (4, 6) the legs are 3 and 4, so the distance is 5. Distance Between Two Points, Exact Answers has ten pairs.

Any slanted segment on a grid is the hypotenuse of a right triangle with a horizontal and a vertical leg. Distance Between Two Points Using a Right Triangle has students draw that triangle for each segment.

Students often add coordinates instead of subtracting them, or add the legs before squaring them. Find the Error in Distance Calculations shows mistakes like these for students to explain and fix.