Graph Transformations — Quick Reference Cheatsheet
A focused companion to the main Graph Transformations topic page on ACT Math.
ACT Math Coordinate Geometry One-page reference
This is a one-page reference for Graph Transformations on the ACT math section. Predict the effect of vertical shifts, horizontal shifts, reflections and dilations. Use it as a printable cheatsheet before test day, or as a refresher right before you attempt the worked questions on the main Graph Transformations topic page.
What this topic is
A Graph Transformations question tests lines, slopes, distance, midpoint, and conic-section equations on the xy-plane. Sketch first, compute second.
Core formulas you must memorise
- Distance: d = √((x₂−x₁)² + (y₂−y₁)²)
- Midpoint: ((x₁+x₂)/2, (y₁+y₂)/2)
- Slope: rise / run
- Parallel: m₁ = m₂ ; Perpendicular: m₁·m₂ = −1
- Circle: (x−h)² + (y−k)² = r²
If any of these formulas are not yet automatic, drill them via the Coordinate Geometry formula sheet. Memorisation is fastest when you write each formula out by hand five times in a row, then quiz yourself the next morning.
How to spot this question type on the test
ACT questions on Graph Transformations typically present in one of three ways: as a pure symbolic problem ("solve for x"), wrapped in a word problem (a real-world scenario you must translate), or hidden inside a longer multi-step question where Graph Transformations is just the first or last step. Train yourself to recognise the signature — a particular word, equation form, or diagram — and you will halve your reading time.
The 30-second decision
A 5-second sketch saves 30 seconds of algebra. Always draw the picture.
If you have 60 seconds before the question
Glance at the answer choices first. If they are widely spaced, estimate; if they are close, you must be exact. Sketch any diagram involved. Identify which of the formulas above applies. Then attempt — and if you cannot finish in 90 seconds, mark and move on. There is no penalty for guessing on either the SAT or the ACT, so always bubble in.
Drill set
Re-attempt the six worked Graph Transformations questions with this cheatsheet open. Then close it and re-attempt them from memory. If you can solve all six without peeking, this topic is locked in.
Related study material
For broader test-prep tactics, see our Graph Transformations strategy guide. For category-wide context, browse all Coordinate Geometry topics. For score-targeted study plans, see the score-band guides.