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Chapter 3: Problem 95

What is the rectangular coordinate system?

Short Answer

Expert verified
The rectangular coordinate system, also known as the Cartesian coordinate system, is a two-dimensional system that is used to represent or plot points on a plane. It consists of two mutually perpendicular lines (the x-axis and y-axis) intersecting at the origin. A point is represented as (x, y), where x is the distance along the x-axis and y is the distance along the y-axis.

Step by step solution

01

Definition of rectangular coordinate system

The rectangular coordinate system, also known as the Cartesian coordinate system, is a two-dimensional system used to represent or plot points on a plane. It consists of two mutually perpendicular lines, known as the x-axis (horizontal line) and y-axis (vertical line), that intersect at a point called the origin.
02

Graphical Representation

In the Cartesian coordinate system, any point is represented as \((x, y)\), where \(x\) is the distance measured along the x-axis and \(y\) is the distance measured along the y-axis. The \(x\) coordinate is called the abscissa and the \(y\) coordinate is called the ordinate.
03

Plotting points in the rectangular coordinate system

To plot a point in this system, for example, \((2,3)\), start at the origin, move two units to the right along the x-axis for positive \(x\) value, and then move three units upwards along the y-axis for positive \(y\) value. The arrived point \((2,3)\) is the location of the point on the plane.

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Most popular questions from this chapter

Solve for \(y\) and put the equation in slope-intercept form. $$y-3=4(x+1)$$

Use a graphing utility to graph in a standard viewing rectangle, \([-10,10,1]\) by \([-10,10,1]\). Then use the \([\text { TRACE }]\) feature to trace along the line and find the coordinates of two points. $$y=\frac{1}{2} x$$

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Use a graphing utility to graph in a standard viewing rectangle, \([-10,10,1]\) by \([-10,10,1]\). Then use the \([\text { TRACE }]\) feature to trace along the line and find the coordinates of two points. $$y=-3 x+2$$
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