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Chapter 1: Problem 62

Explain how to plot a point in the rectangular coordinate system. Give an example with your explanation.

Short Answer

Expert verified
To plot a point in the rectangular coordinate system, start at the origin, move along the \(x\)-axis the number of units equal to the \(x\)-coordinate, then from there, move up or down along the \(y\)-axis the number of units equal to the \(y\)-coordinate. For our example, the point \((3, -2)\) would be plotted by moving right 3 units from the origin and then down 2 units.

Step by step solution

01

Understand the coordinate system

In the rectangular coordinate system, each point is identified by a pair of coordinates written as \((x, y)\), where \(x\) is the horizontal coordinate, and \(y\) is the vertical coordinate. The \(x\)-coordinate states how far to travel along the \(x\)-axis from the origin. If \(x\) is positive, move to the right, if \(x\) is negative, move to the left. The \(y\)-coordinate states how far to move along the \(y\)-axis from where you landed after moving due to the \(x\)-coordinate. If \(y\) is positive, move upwards, if \(y\) is negative, move downwards.
02

Identify the point to be plotted

The next step is to identify the point to be plotted. Let's take an example point \((3, -2)\). Here, 3 is the \(x\)-coordinate and -2 is the \(y\)-coordinate.
03

Plot the point on the coordinate system

Starting at the origin (where the \(x\) and \(y\) axis intersect), move right 3 units along the \(x\)-axis (since our \(x\) coordinate is 3), then from there, move down 2 units along the \(y\)-axis (since our \(y\) coordinate is -2). Mark this position as our point \((3, -2)\).

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