Problem 8 - Precalculus Essentials

Question

Plot the given point in a rectangular coordinate system. $$(3,-2)$$

Step-by-Step Solution

Answer

The point (3,-2) is plotted three units to the right and two units below the origin in a rectangular coordinate system.

Step 1: Recognize the coordinate pair

The order pair is given as \( (3,-2) \). In a standard coordinate pair like this, the first number is the x-coordinate and the second number is the y-coordinate. They represent the position of a point along the x-axis and y-axis of a graph respectively.

Step 2: Start plotting the point

Starting from the origin (the point where the x-axis and y-axis intersect, also represented by (0,0)), move three units to the right since the x-coordinate is positive 3. This takes you to the point (3, 0) on the graph.

Step 3: Complete the plotting of the point

From the current position, since the y-coordinate is negative, move two units downwards to reach the point (3, -2). This is because a negative y-coordinate represents a position below the x-axis. The order pair (3, -2) is now plotted on the graph.

Step 4: Validate the point

Check the plotted point to ensure it is in line with the x = 3 line vertically and y = -2 line horizontally on the graph. If yes, then it is the correct point.