Problem 50 - 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 on the rectangular coordinate system, start from the origin, move along the x-axis to the distance equal to x-coordinate, then move vertically by the y-coordinate. For example, for the point (3,2), start at the origin, move 3 units to the right on the x-axis, then 2 units upwards.

Step 1: Understanding Coordinates

First, understand what coordinates are. In the Cartesian coordinate system, we usually express a point in the form of (x, y). Here, 'x' is the distance along the horizontal axis (x-axis) and 'y' is the distance along the vertical axis (y-axis). The x-value is called the abscissa and the y-value is called the ordinate of the point.

Step 2: Recognize the Origin

In the rectangular coordinate system, the origin is the point where both x and y coordinates are zero, represented by (0,0). This is the point of intersection of the x-axis and y-axis.

Step 3: Plotting a Point

To plot a point, start from the origin. If x is positive, move right along the x-axis. If it's negative, move left. Then, move parallel to the y-axis. If y is positive, move up, and if y is negative, move down. The reached point after these movements is the required point.

Step 4: Example

Let's plot a point (3, 2). Start at the origin, move 3 units to the right on the x-axis (since x is 3 in the given point), then 2 units up parallel to the y-axis (since y is 2). This will plot the point (3, 2).