Concept 5

Use coordinate geometry (distance, midpoint, slope; parallel/perpendicular lines).

Use slope, midpoint, and distance as the main coordinate-geometry tools.

Core Idea

On the coordinate plane, slope controls direction, midpoint averages coordinates, and distance comes from the Pythagorean theorem. Parallel lines share slope, while perpendicular lines have negative reciprocal slopes.

Understanding

Rule: Coordinate geometry is easier when you separate the core tools. Use slope to compare direction, midpoint to find the center between two endpoints, and distance when the question asks for length. For line relationships, parallel means equal slopes and perpendicular means slopes whose product is $- 1$ , when both are defined.

Keep subtraction order consistent in the slope formula so signs do not flip by accident.

Question

Worked Example

Points $𝐴 (1, 2)$ and $𝐵 (5, 10)$ determine line $𝐴 𝐵$ . What is the slope of a line perpendicular to $𝐴 𝐵$ ?

Select an answer to see the explanation