The distance and midpoint formulas
- Six blocks of driving, four different flights — 3 tasks
- Making the triangle that settles it — 3 tasks
- From two points to a length — 6 tasks
- How long, and where is the centre — 3 tasks
- The points that are equally far from both — 3 tasks
- Practice — 30 tasks
- Summary — 2 tasks
- Cool-down — 3 tasks
Classroom activities
Things a class does rather than writes on. Each one is a finished PDF: print it, cut it up if it says so, and hand it round.
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Distance Formula, Midpoint Formula, or Along the Grid? Choosing the Tool — Cut & Glue Sort 25 minutes, including the cutting · 5 sheets
12 short questions about two points in the coordinate plane. Students do not compute: they sort each one by the tool that answers it. The distance formula for a straight line, the midpoint formula for the point halfway, or neither, because the path must stay on the grid lines and its length is across plus up.
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Distance and Midpoint Formulas: How Long and Where? — Answer Maze 10–15 minutes · 4 sheets
8 boxes on one page. Each gives two points and asks either how far apart they are or where the midpoint is, and the route asks both questions of the same pairs. Distances stay exact, in simplest radical form; midpoints are pairs. The wrong answers are the common mistakes: leaving out the root, mis-pairing the coordinates, losing a minus sign, subtracting and halving. The row of box numbers at the foot is the check.
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The Distance Formula: Is It Set Up Right? — Mystery Picture 25–35 minutes · 5 sheets
25 squares, each with two points A and B and a setup for the distance such as across = 5 − (−3), up = 2 − 7, AB = √(across² + up²). Students compute nothing: they check that the x-coordinates are paired with x and the y-coordinates with y, that every minus sign is kept, and that the root covers the sum. Fill it or leave it white, and a picture appears.
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The Distance Formula: Exact Answers in Simplest Radical Form — Scavenger Hunt a full class period · 13 sheets
16 cards around the room, each with two points in the coordinate plane, some with negative coordinates. Students find the distance with the distance formula and leave it exact, in simplest radical form. Forgetting the square root, or subtracting each point’s own x and y, lands on a card that sends the group back, and a clean run is 8 lines on the record sheet.