Coordinate geometry

Distance, midpoint, gradient and the equation of a line through two points. About 9 minutes, GCSE.

What you will do

  1. Points, steps and Pythagoras. Two points are separated by a step across (Δx) and a step up (Δy). Every formula in this lesson is built from those two steps.
  2. Distance, midpoint and gradient. The distance is the hypotenuse of the step triangle. The midpoint is the average of the coordinates. The gradient is Δy ÷ Δx.
  3. The equation of the line. Use y = mx + c: find the gradient m, then put one point in to find c.
  4. A vertical line. When the two x-coordinates are equal, Δx = 0 and the gradient is undefined: the line is x = a constant.
  5. Perpendicular lines. Lines at right angles have gradients whose product is -1. Flip the gradient and change its sign.

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