Maths · Coordinate geometry. The idea in plain words, the rules to remember, the mistake to avoid and a worked example, written and checked by Mega Lecture.
Two lines are perpendicular when they cross at a right angle (90°). On a graph you do not need to measure the angle: the gradients tell you. If you multiply the gradients of two perpendicular lines, the answer is always −1.
So the gradient of the perpendicular line is the negative reciprocal: turn the gradient upside down and change its sign. A gradient of 2 becomes −1/2, and a gradient of −3/4 becomes 4/3.
Always write the line as y = mx + c first, so that you read the correct gradient. A perpendicular bisector of AB is the line through the midpoint of AB that is perpendicular to AB.
Students change only the sign (3 becomes −3) or only turn the gradient upside down (3 becomes 1/3). You must do both: 3 becomes −1/3. Check by multiplying the two gradients to get −1.
Answer: y = −x/3 + 3
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