Use a polar coordinate system like the one shown for Exercises 1–10 to plot each point with the given polar coordinates. (2, 45°)

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Understand that the polar coordinates are given in the form \((r, \theta)\), where \(r\) is the distance from the origin and \(\theta\) is the angle measured from the positive x-axis (polar axis) in degrees.

Identify the given coordinates: \(r = 2\) and \(\theta = 45^\circ\).

Locate the angle \(45^\circ\) on the polar coordinate system. This angle is measured counterclockwise from the positive x-axis.

From the origin, move along the line that makes a \(45^\circ\) angle with the positive x-axis.

Mark the point at a distance of 2 units from the origin along this line. This is the point with polar coordinates \((2, 45^\circ)\).

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Polar Coordinate System

The polar coordinate system represents points in a plane using a distance and an angle from a fixed origin. Each point is defined by (r, θ), where r is the radius or distance from the origin, and θ is the angle measured in degrees or radians from the positive x-axis.

Plotting Points Using Polar Coordinates

To plot a point given in polar coordinates (r, θ), start at the origin, measure the angle θ counterclockwise from the positive x-axis, then move outward along that direction by the distance r. This locates the point accurately on the plane.

Angle Measurement in Degrees

Angles in polar coordinates are often given in degrees, measured counterclockwise from the positive x-axis. Understanding how to interpret and measure these angles is essential for correctly positioning points in the polar plane.

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