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Coordinate geometry
Distance, midpoint, slope and the equation of a line.
Coordinates turn geometry into algebra. The distance between two points is Pythagoras; the midpoint is an average; the slope is rise over run; and slope plus a point gives the line's equation.
Worked example: line through (0,1) and (2,5)
Step by step
- m = \frac{\Delta y}{\Delta x} = \frac{4}{2} = 2
Slope = rise over run.
- y - 1 = 2(x - 0)
Point-slope form through P.
- y = 2 x + 1
Slope-intercept form.
Reveal the answer
y = 2 x + 1