Coordinate Geometry Summary

ACT Math · Axiom Academy

SUMMARY Coordinate Geometry Summary Points, lines, circles, and curves on the plane — the full arc of Unit 4, reviewed in one pass. Every coordinate-geometry question — slope, distance, midpoint, circles, transformations — reduces to plugging two or three numbers into one memorized formula. Nothing here requires improvisation. Slope drives line relationships: equal slopes → parallel , slopes multiplying to -1 → perpendicular . The distance formula is the Pythagorean theorem wearing coordinates; recognizing a 3-4-5, 5-12-13, 8-15-17, or 7-24-25 triple in the legs skips the square root entirely. Circle, ellipse, and parabola equations all name their key point (h,k) directly — the only trap is the built-in sign flip: (x+3)^2 means h=-3 , not 3 . Transformations split cleanly on one question: is the change inside the parentheses (touches x , acts backwards) or outside (touches y , acts as written)? Core Concept Slope & Linear Equations Slope measures steepness between any two points and drives every line question on the test. Slope-intercept form y = mx + b names the slope and y -intercept directly, so most ACT line questions are really just "read m and b off the equation, or off two points." When to use: any question comparing two lines, or asking to write a line's equation. Watch out for: keep the y 's and x 's in the same order — (y_2-y_1)/(x_2-x_1) , never flipped. Core Concept Parallel & Perpendicular Lines

This is the written version of the interactive lesson above. See the full ACT Math course.