ACT Math · 15% of the test
Coordinate Geometry
Coordinate Geometry covers lines and slopes, distance and midpoint, parallel and perpendicular lines, the equation of a circle, and an introduction to conic sections.
What's actually tested
These items live in the (x, y) plane. They test geometric facts expressed in coordinate terms — for example, perpendicular lines have slopes that multiply to −1 — and reward students who can switch fluently between graph and equation.
Subtopics
Click any subtopic to see filed practice questions, worked solutions, and a short tactical guide.
Lines, slopes, and intercepts
Slope, point-slope form, and parallel/perpendicular lines.
Distance and midpoint
Distance and midpoint between two points.
Circles in the coordinate plane
Standard equation, center, and radius of a circle.
Introduction to conics
Recognizing parabolas, ellipses, and hyperbolas from equations.
Sample practice questions in this topic
- Easy Lines, slopes, and intercepts What is the slope of the line passing through (5, 3) and (-3, -4)?
- Easy Lines, slopes, and intercepts What is the slope of the line passing through (-1, 5) and (-5, 0)?
- Medium Lines, slopes, and intercepts What is the slope of the line passing through (4, 0) and (5, 1)?
- Medium Lines, slopes, and intercepts What is the slope of the line passing through (0, 0) and (-4, -1)?
- Medium Lines, slopes, and intercepts What is the slope of the line passing through (-1, 3) and (-4, 3)?
- Hard Lines, slopes, and intercepts What is the slope of the line passing through (5, 4) and (2, -4)?
- Easy Lines, slopes, and intercepts What is the slope of the line passing through (4, 0) and (-4, -3)?
- Easy Lines, slopes, and intercepts What is the slope of the line passing through (-2, -1) and (-5, -4)?
- Medium Lines, slopes, and intercepts What is the slope of the line passing through (-3, 3) and (-5, -5)?
- Medium Lines, slopes, and intercepts What is the slope of the line passing through (4, -4) and (5, -3)?
- Medium Lines, slopes, and intercepts What is the slope of the line passing through (0, 5) and (4, -2)?
- Hard Lines, slopes, and intercepts What is the slope of the line passing through (5, -1) and (4, 4)?
See all 56 questions in Coordinate Geometry →
How students lose points here
Mixing up parallel-vs-perpendicular slope rules, sign errors in the distance formula, and using diameter when the equation calls for radius. The good news: nearly every common mistake on this topic comes from one of three or four recurring patterns. Spend an hour reviewing those patterns and your accuracy on this topic typically jumps two or three percentage points immediately, which on a balanced test is worth ten to twenty scaled score points depending on your band.
How to study this topic
Memorize the slope, distance, midpoint, and circle formulas. They are short and used constantly. A reasonable session looks like fifteen practice items, untimed, with you reading the worked solution after every one — even the questions you got right, because being right by accident teaches nothing. After two or three such sessions, attempt a timed mini-set of ten items. If your accuracy stays above 80%, move on. If it doesn't, drill the lowest-accuracy subtopic for another session before you push forward.