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Math Example--Coordinate Geometry--Coordinate Systems: Example 31

Math Example--Coordinate Geometry--Coordinate Systems: Example 31

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Topic

Geometry

Description

This example focuses on plotting points in the third and fourth quadrants of the complex plane. The image displays four points: (-1, -i), (-5, -3i) in the third quadrant, and (2, -8i), (9, -3i) in the fourth quadrant. These points represent complex numbers with negative imaginary parts and varying real parts.

Understanding how to plot points across different quadrants is essential for a comprehensive grasp of complex number theory and coordinate geometry. This example helps students visualize how points with negative imaginary parts are positioned on the complex plane, with the real part determining whether they fall in the third or fourth quadrant.

By providing examples that span the lower half of the complex plane, students can develop a deeper understanding of the relationship between complex numbers and their geometric representation. This approach reinforces the concept of how the signs of real and imaginary parts determine a point's quadrant.

Teacher's Script: Look carefully at how these points are plotted in the third and fourth quadrants. Notice that all points have negative imaginary parts, but the real parts determine which quadrant they're in. Can you explain why changing the sign of the real part moves a point from the third to the fourth quadrant? Let's discuss how this relates to our understanding of both complex numbers and coordinate geometry.

For a complete collection of math examples related to Coordinate Systems click on this link: Math Examples: Coordinate Systems Collection.

Common Core Standards CCSS.MATH.CONTENT.6.NS.C.8
Grade Range 6 - 8
Curriculum Nodes Geometry
    • Coordinate Geometry
        • Coordinate Systems
Copyright Year 2013
Keywords coordinate geometry, coordinate systems, coordinate system