Straight lines: mid-points, equations and straight-line form
Watch the whole lecture free
Make a free account to watch every lecture to the end: 1 worked example, 5 practice questions, 2 real past-paper questions with the answers explained, the mistakes that lose marks, the full-marks tip, a one-card summary and a quick quiz.
That was the teaching part. The rest of this lecture is free with an account: 1 worked example, 5 practice questions, 2 real past-paper questions with the answers explained, the mistakes that lose marks, the full-marks tip, a one-card summary and a quick quiz.
No password needed now: we email you a link to set one. Already have an account? Sign in, then come back to this page.
The teaching part (1 min) is free to watch. A free account opens the whole lecture: 1 worked example, 5 practice questions, 2 real past-paper questions with the answers explained, the mistakes that lose marks, the full-marks tip, a one-card summary and a quick quiz.
What this lecture covers
- Three facts about two points
- Mid-point, length and gradient
- The equation of a line
Read the transcript of the teaching part
Last time
Before we start: last time, in Laws of logarithms and solving equations, you learned these points. Here they are again on one card. Keep them in mind, because today builds on them.
Three facts about two points
Give me two points. I can tell you the middle, the distance, and the slope. From those three facts you can build the line, a perpendicular bisector, or even the formula behind a graph that is not a straight line.
Mid-point, length and gradient
The mid-point is the average of the coordinates. The length is Pythagoras on the differences. The gradient is the rise over the run. Perpendicular lines have gradients that multiply to minus one.
The equation of a line
With gradient m through the point x1, y1, the equation is y minus y1 equals m, bracket x minus x1. Parallel lines share a gradient. Perpendicular lines have the negative reciprocal. When asked for integers, rearrange to a x plus b y plus c equals zero.
How often it comes up
How often Cambridge has asked each part, counted by ExamYard from every past paper in its question bank: Mid-points, lengths and perpendicular bisectors · Straight-line form: finding the unknown constants.
The whole chapter: Simultaneous Equations, Straight-Line Graphs.
Chapter 7: Straight-line graphs
- Straight lines: mid-points, equations and straight-line form 5 min
Also for O Level Additional Maths 4037
Which topics come up most in O Level Additional Maths 4037 past papers, counted from every paper since 2004.