Geometry

What you'll learn

• Calculate distance between two points using the distance formula
• Find the midpoint of a line segment
• Determine whether lines are parallel (equal slopes) or perpendicular (negative reciprocal slopes)
• Write equations of lines given various information (two points, slope and point, etc.)
• Graph linear and simple nonlinear equations on the coordinate plane

Key concepts

Coordinate geometry connects algebra and geometry on the xy-plane. The distance between points (x₁,y₁) and (x₂,y₂) is √((x₂−x₁)² + (y₂−y₁)²). The midpoint is ((x₁+x₂)/2, (y₁+y₂)/2). Parallel lines have equal slopes; perpendicular lines have slopes that are negative reciprocals (e.g., 2 and −1/2). The ACT frequently asks you to find the equation of a line given two points, or to determine the relationship between two lines. Coordinate geometry questions make up roughly 15% of the Math section.

Pro tips

• Memorize the distance and midpoint formulas. They appear on nearly every ACT.
• Slopes of horizontal lines are 0; slopes of vertical lines are undefined.
• If a question asks for the line perpendicular to y = 3x + 1, the slope is −1/3.