知识点 5

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

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

核心知识

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.

深入理解

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.

题目

示例解析

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

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