GRE Coordinate Geometry
The coordinate plane shows up all over GRE Quant, and almost everything comes back to one idea: slope. Get comfortable reading a line, and these questions become quick. Drag the tool below to feel how slope and intercept shape a line.
Slope and slope-intercept form
Slope is rise over run: (y2 − y1) / (x2 − x1). Every line can be written as y = mx + b, where m is the slope and b is where the line crosses the y-axis. Drag the two handles to change the slope and the intercept and watch the equation update live.
Slope & intercept
Reading left to right, which way does a line tilt when its slope m is NEGATIVE?
The rules worth memorizing
- Positive slope rises left to right; negative falls; horizontal is 0; vertical is undefined.
- Parallel lines: equal slopes.
- Perpendicular lines: slopes are negative reciprocals (product is −1).
- Distance: √((x2−x1)² + (y2−y1)²), which is the Pythagorean theorem in disguise.
- Midpoint: average the x's and the y's: ((x1+x2)/2, (y1+y2)/2).
Frequently asked questions
How do you find the slope of a line on the GRE?
Slope is rise over run: take two points and compute (y2 − y1) / (x2 − x1). A positive slope rises left to right, a negative slope falls, a horizontal line has slope 0, and a vertical line has an undefined slope.
What is slope-intercept form?
y = mx + b, where m is the slope and b is the y-intercept (where the line crosses the y-axis). It is the fastest way to read a line's behavior and to graph it.
How do I tell if lines are parallel or perpendicular?
Parallel lines have equal slopes. Perpendicular lines have slopes that are negative reciprocals (their product is −1), for example 2 and −1/2.
What are the distance and midpoint formulas?
Distance between (x1,y1) and (x2,y2) is √((x2−x1)² + (y2−y1)²), which is just the Pythagorean theorem. The midpoint is ((x1+x2)/2, (y1+y2)/2).
Practice coordinate geometry, adaptively
Grezi drills you on lines, slopes, and the coordinate plane with real GRE questions and an AI tutor that finds your blind spots.
More GRE Quant: all topics, formula sheet.