Math 1 · Unit 4 · Lesson 2
Perpendicular Lines and the Negative Reciprocal
Perpendicular lines cross at a right angle, a square corner. Turn a line a quarter turn and its rise and run trade places, and it leans the other way: the new slope is the negative reciprocal, flip the fraction and change the sign. Two slopes that multiply to make negative one are always perpendicular. Then write a perpendicular line through a point.
The big idea
Perpendicular lines meet at a right angle, and their slopes are tied together by a quarter turn. Turn a staircase of rise 2 and run 3 a quarter turn and the rise and the run trade places, while the lean reverses: slope two thirds becomes slope negative three halves. That is the negative reciprocal, flip the fraction (the reciprocal, the multiplicative inverse from Unit 1) and change the sign, and the quick check is that the two slopes multiply to negative one. The one pair the rule cannot reach is a horizontal line and a vertical line, since you cannot flip zero, and you handle that pair by sight. Writing a perpendicular line through a point is then the same two moves as Lesson 1 with one change: take the negative reciprocal for m, then use the point to find b.
The parts of this lesson
Each part is its own short page. Go in order, or pick the one you need.
Printables
One page with the quarter-turn picture, the negative reciprocal, the product check, the special pair, the two moves for a perpendicular line, and a worked example. Plus a worksheet with grids and an answer key, and a short lesson plan.