Coordinate geometry: watch it solved step by step

Distance, midpoint, gradient and the equation of the line through two points, with the graph. Level: GCSE. Type any problem of this kind and the Lab works it out and animates every move, with a plain-words explanation of why.

Worked example: (0, 0) to (3, 4)

1. The two points. Name the points A and B. Everything below comes from how far apart they are across (Δx) and up (Δy).
2. The horizontal and vertical steps. Subtract the coordinates: how far you move across, and how far up.
3. Distance (Pythagoras). The straight line AB is the hypotenuse of a right-angled triangle with legs Δx and Δy.
4. Midpoint. The point halfway between: average the x-coordinates and average the y-coordinates.
5. Gradient. Gradient = how far up for each step across.
6. Equation of the line. Use y = mx + c and put point A in to find c.
7. A perpendicular line. Lines at right angles have gradients that multiply to -1: flip the gradient and change its sign.

Answer: distance = 5; midpoint = (3/2, 2); gradient = 4/3; y = 4/3x

Practise coordinate geometry with problems the Lab marks for you.