Straight lines: mid-points, equations and straight-line form
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The teaching part (1 min) is free to watch. A free account opens the whole lecture: 4 worked examples, 5 practice questions, 1 real past-paper question with the answer 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 Reversing transformations, sketching transformed graphs and inverses, 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.
Chapter 1.3: Coordinate geometry
- Straight lines: mid-points, equations and straight-line form 6 min
- The equation of a circle and two circles 6 min
- Tangents to a circle and a line and a circle 6 min
Also for A Level Maths 9709 Paper 1
Which topics come up most in A Level Maths 9709 Paper 1 past papers, counted from every paper since 2004.