Problem 62 - College Algebra

Question

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

Step-by-Step Solution

Answer

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 1: 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.

Step 2: 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.

Step 3: 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 \((3, -2)\).