Coordinate Geometry
The xy-plane: lines, slope, distance, midpoint, conic sections and graph transformations.
8 skill topics sit under Coordinate Geometry on the ACT Math taxonomy. Each one has its own dedicated page with concept notes and six worked practice questions. Work through the list top to bottom, or jump straight to the topic you struggle with.
This category accounts for a meaningful slice of your overall math score, so spend the time. The fastest way to gain points is to convert one weak topic per week into a strong one — not to skim every topic at surface depth.
Need the formulas at a glance? See the Coordinate Geometry formula sheet. Studying for a specific score range? Use the score-band guides to focus on the topics that move the needle for your current score.
All Coordinate Geometry topics
Midpoint and Distance
Use M = ((x₁+x₂)/2,(y₁+y₂)/2) and d = √((x₂−x₁)² + (y₂−y₁)²) on the xy-plane.
Open topic
Slope-Intercept Form
Read slope and y-intercept directly from y = mx + b and write equations of lines.
Open topic
Parallel and Perpendicular Lines
Use equal slopes for parallel lines and opposite-reciprocal slopes for perpendicular lines.
Open topic
Conic Sections
Recognise the equations of circles, ellipses, parabolas and hyperbolas.
Open topic
Graphing Parabolas
Use the vertex form y = a(x − h)² + k to sketch a parabola quickly.
Open topic
Graphing Circles
Read centre and radius from (x − h)² + (y − k)² = r².
Open topic
Graph Transformations
Predict the effect of vertical shifts, horizontal shifts, reflections and dilations.
Open topic
Intersections of Graphs
Solve f(x) = g(x) algebraically or graphically to find points where two curves meet.
Open topic
Recommended study order
If this category is brand new to you, start with the first three topics in the list above — they tend to be the most foundational. Then work outward to the others. If you're already comfortable, go straight to a recent past paper, identify which Coordinate Geometry question you missed, and drill that specific topic page.
For broader test-prep advice, see our study tips. For real test reference, browse the ACT Math past paper index.