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# ZingPath: Graphs of Linear Equations

## Determining the Coordinate Plane                 Searching for

## Graphs of Linear Equations

Learn in a way your textbook can't show you.
Explore the full path to learning Graphs of Linear Equations ### Lesson Focus

#### Determining the Coordinate Plane

Algebra-1

You get to learn how to work with and solve problems that involve regions of polygons in the coordinate plane.

### Now You Know

After completing this tutorial, you will be able to complete the following:

• Define the Cartesian plane as a set of points.
• Identify the axes.
• Write the coordinates of points on the plane.
• Identify quadrants based on the signs of the coordinates of the points in that region.

### Everything You'll Have Covered

What is the Cartesian plane?

~ The plane determined by two perpendicular axes is the Cartesian plane.

In the Cartesian plane, which axis is the x-axis and which axis is the y-axis?

~ The horizontal axis is the x-axis and the vertical axis is the y-axis.

What are the Cartesian coordinates of a point in the Cartesian plane? How do we find a point's Cartesian coordinates when it is plotted in the Cartesian plane?

~ The Cartesian coordinates of a point is an ordered pair of numbers, . The first component, in this case the number a, is called the horizontal or x-coordinate of the point, and the second component, in this case the number b, is called the vertical or y-coordinate of the point. If a point A is plotted in the Cartesian plane, we draw line segments from A perpendicular to each of the coordinate axes. The number on the horizontal axis where the drawn line segment intersects the horizontal axis is the horizontal coordinate of A. The number on the vertical axis where the drawn line segment intersects the vertical axis is the vertical coordinate of A.

What is special about the Cartesian coordinates of a point that lies on the horizontal axis? What is special about the Cartesian coordinates of a point that lies on the vertical axis? What are the Cartesian coordinates of the origin?

~ If a point is on the horizontal axis, then its vertical coordinate is 0. If a point is on the vertical axis, then its horizontal coordinate is 0. The origin is on both axes, so its Cartesian coordinates are (0,0).  ~ The points have the following Cartesian coordinates: A(-2, -5), B(-4, 1), C(5, 0), and D(4, -2). Recall that Quadrant III is the region with points that have negative horizontal coordinates and negative vertical coordinates. Only point A has a negative horizontal coordinate and a negative vertical coordinate, so point A is the only point in Quadrant III. ### Tutorial Details

 Approximate Time 2 Minutes Pre-requisite Concepts Students should be able to define Cartesian coordinate system, Cartesian plane, and quadrants. Course Algebra-1 Type of Tutorial Animation Key Vocabulary Cartesian coordinates of a point, Cartesian coordinate system, cartesian plane