Locate each point in a coordinate system. Draw a ray from...

Locate each point in a coordinate system. Draw a ray from the origin through the given point. Indicate with an arrow the angle in standard position having least positive measure. Then find the distance $r$ from the origin to the point, using the distance formula of Section 2.1 $$(\sqrt{2},-\sqrt{2})$$

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Key Concepts

Ray

A ray is a part of a line that starts at a specific point and extends infinitely in one direction. In the context of coordinate geometry, drawing a ray from the origin through a given point helps visualize the direction corresponding to the point and is essential for understanding angles in standard position.

Standard Position Angle

An angle in standard position is one whose vertex is at the origin with its initial side along the positive x-axis. The angle is measured in a counterclockwise direction to the terminal side. The least positive measure of the angle is the smallest positive angle that uniquely describes the terminal ray's direction.

Coordinate System

The coordinate system is a framework in the plane consisting of an x-axis and a y-axis, which intersect at the origin. It allows positions of points to be expressed as ordered pairs (x, y), facilitating graphical representation of algebraic concepts and relationships.

Distance Formula

The distance formula is derived from the Pythagorean theorem and is used to compute the straight-line distance between two points in a coordinate plane. For any two points, (x1, y1) and (x2, y2), the distance is calculated by taking the square root of the sum of the squares of the differences in their x-coordinates and y-coordinates.

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