Lines, line segments, and rays

Learning Objectives Define and differentiate between lines, line segments, and rays using proper geometric notation. Represent lines, line segments, and rays on the coordinate plane given their defining points. Calculate the length of a line segment using the Distance Formula. Determine the coordinates of the midpoint of a line segment using the Midpoint Formula. Write the equation of the infinite line that contains a specific line segment or ray. Apply the concept of slope to determine if a point lies on a specific ray or line segment. Ever wonder how GPS calculates the shortest route or how a game designer programs a laser beam's path? 🗺️ It all starts with the fundamental building blocks: lines, line segments, and rays! This tutorial explores the precise definitions...

TermDefinitionExample LineA straight, one-dimensional figure that has no thickness and extends endlessly in both directions. It is defined by two distinct points.The line passing through points A(1, 2) and B(5, 4) is denoted as $\overleftrightarrow{AB}$. Line SegmentA part of a line that is bounded by two distinct end points, and contains every point on the line between its endpoints.The line segment with endpoints C( -2, 1) and D(3, 1) is denoted as $\overline{CD}$. It has a finite length. RayA part of a line that has one endpoint and extends infinitely in one direction.The ray starting at endpoint P(0, 3) and passing through Q(2, 4) is denoted as $\overrightarrow{PQ}$. The order of the letters matters. EndpointA point that marks the end of a line segment or the beginning of a ray.For t...

The Distance Formula Given two points $(x_1, y_1)$ and $(x_2, y_2)$, the distance $d$ between them is: $d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$ Use this formula to calculate the length of a line segment. This formula is derived from the Pythagorean theorem. The Midpoint Formula Given a line segment with endpoints $(x_1, y_1)$ and $(x_2, y_2)$, the midpoint $M$ is: $M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)$ Use this formula to find the exact coordinates of the center point of a line segment. It is essentially the average of the x-coordinates and the average of the y-coordinates. The Slope Formula Given two points $(x_1, y_1)$ and $(x_2, y_2)$ on a line, the slope $m$ is: $m = \frac{y_2 - y_1}{x_2 - x_1}$ Use this formula to find the slope of the l...