Math 1 · Unit 11
Midpoint and Distance on a Coordinate Plane
Four lessons: distance (the Pythagorean theorem on the grid), midpoint (meeting in the middle), perimeter and area from coordinates, and proving shapes with coordinates. Three tools answer three questions about a segment: how steep (slope), how long (distance), and where is the middle (midpoint). Every formula is a shortcut for something you can draw.
Distance, the Pythagorean Theorem on the Grid
How long is it? Count a horizontal or vertical segment. For a slanted one, draw the right triangle under it and use the Pythagorean theorem: square the legs, add, and take the square root. Do a few by drawing, notice the pattern, and that is the distance formula.
Start Unit 11, Lesson 1Midpoint, Meeting in the Middle
Where is the middle? The midpoint is halfway along a segment: average the x's and average the y's, as stacked fractions. Jennifer and Jane meet at (12, 8). Then run it backward: from the midpoint and one endpoint, find the other by the step way or the equation way.
Start Unit 11, Lesson 2Perimeter and Area from Coordinates
Perimeter is distance for every side, then add: a countable rectangle, then a pentagon with three sides of 5 and two square roots. Area: length times width for a rectangle, one half base times height for a triangle, with the height checked by slopes first. The box method for everything else.
Start Unit 11, Lesson 3Proving Shapes with Coordinates
All three tools together. Slope for parallel and perpendicular, distance for equal sides, midpoint for the diagonals. Prove MNPQ is a square, find the missing corner of a rectangle from the shared midpoint of its diagonals, and write proofs as clear sentences that name the tool and the result.
Start Unit 11, Lesson 4Printables for Unit 11
Study guides, worksheets with answer keys, and lesson plans for every lesson in this unit.