Coordinate Geometry on the GRE

Slope: m = (y2-y1)/(x2-x1)

Positive slope: line goes up. Negative: down. Zero: horizontal. Undefined: vertical.

Slope-intercept: y = mx + b

m = slope, b = y-intercept

Parallel lines: Same slope, different intercepts.

Perpendicular lines: Slopes multiply to -1 (negative reciprocals).

Distance formula: d = sqrt((x2-x1)2 + (y2-y1)2)

This IS the Pythagorean theorem applied to coordinates.

Midpoint: ((x1+x2)/2, (y1+y2)/2)

Circle equation: (x-h)2 + (y-k)2 = r2

Center = (h,k), radius = r

GRE favorite: Questions about which quadrant a point or line falls in. Remember: Q1 (+,+), Q2 (-,+), Q3 (-,-), Q4 (+,-).

Reference:

Wikipedia: Coordinate Geometry

https://en.wikipedia.org/wiki/Coordinate_geometry