Lines, line segments, and rays

Learning Objectives Define and visually differentiate between a line, a line segment, and a ray. Correctly name lines, line segments, and rays using proper geometric notation. Identify and model these geometric figures in diagrams and real-world contexts. Understand and apply the concept of collinear points and the Segment Addition Postulate. Calculate the midpoint of a line segment on a coordinate plane using the Midpoint Formula. Calculate the length of a line segment on a coordinate plane using the Distance Formula. How does your phone's GPS calculate the straight-line distance between two locations? 🗺️ It all begins with the fundamental geometric concepts of points and the paths that connect them! This tutorial will explore the essential building blocks of all geom...

TermDefinitionExample LineA one-dimensional figure made up of a straight path of points that extends infinitely in opposite directions. It has no thickness and no endpoints.A line passing through points A and B is denoted as ↔AB. The arrows indicate it continues forever in both directions. Line SegmentA part of a line that is bounded by two distinct endpoints. It contains these endpoints and all the points on the line between them. A line segment has a specific, measurable length.A line segment with endpoints A and B is denoted as AB (with a bar over it). Its length is denoted as AB. RayA part of a line that has one endpoint and extends infinitely in one direction. The endpoint is always named first.A ray starting at point A and passing through point B is denoted as →AB. It starts at A a...

Segment Addition Postulate If three points A, B, and C are collinear and B is between A and C, then AB + BC = AC. Use this postulate to find the length of a part of a segment or the whole segment when you know the lengths of the other parts. It essentially states that the two smaller pieces add up to the whole. Midpoint Formula For a line segment with endpoints (x₁, y₁) and (x₂, y₂), the midpoint M is given by the formula: M = ( (x₁ + x₂)/2 , (y₁ + y₂)/2 ). Use this formula in coordinate geometry to find the exact center point of a line segment. It works by averaging the x-coordinates and averaging the y-coordinates. Distance Formula The distance, d, (or length) of a line segment with endpoints (x₁, y₁) and (x₂, y₂) is given by the formula: d = \sqrt{(x₂ - x₁)² + (y₂ -...