Problem 4 - Algebra 1

Question

Plot the ordered pairs in a coordinate plane. (GRAPH CANNOT COPY) $$A(4,-1), B(5,0)$$

Step-by-Step Solution

Answer

Point A is positioned in the fourth quadrant in the coordinate plane and point B is positioned on the x-axis. The correct graph would have point A at the position (4,-1) and B at the position (5, 0).

Step 1: Understanding the Coordinate System

Firstly, we must understand the Coordinate System. It consists of two perpendicular axes: the horizontal axis is called the x-axis, and the vertical axis is called the y-axis. The point where these axes intersect is called the origin, denoted as \( (0,0) \). Every point in the plane can be specified by an ordered pair of numbers.

Step 2: Plotting Point A

Point A has coordinates (4,-1). The first coordinate is the x-value, which means we start at the origin and move 4 units to the right along the x-axis. The second coordinate is the y-value which, since it's negative, means we should move down 1 unit from our x-coordinate position (4,0) along the y-axis. So, point A is located in the fourth quadrant of the coordinate plane.

Step 3: Plotting Point B

Now let's plot point B, which has coordinates (5, 0). Starting from the origin, we move right 5 units along the x axis, since the x coordinate is 5. However, since the y coordinate is 0, it tells us we don't need to move up or down along the y axis from our x-coordinate position. Therefore, point B lies on the x-axis.

Key Concepts

Ordered Pairs

An ordered pair is essentially a combination of two numbers placed together in a specific order, like this:

• (x, y)

The first number, known as the x-coordinate, shows how far we should move from the origin along the horizontal axis. The second number, called the y-coordinate, indicates the movement up or down from x along the vertical axis.
The order is vital because changing the sequence of numbers changes the location of the point. For instance, in the ordered pair (4, -1), 4 is associated with the x-axis and -1 is associated with the y-axis. This pair helps pinpoint an exact location on the plane.
Remember: The order in 'ordered pairs' is what keeps things running smoothly in navigating the xy-coordinate plane.

Plotting Points

Plotting points on a coordinate plane involves identifying a unique position corresponding to an ordered pair. Here’s how it’s done:

• Begin at the origin (0,0)
• Move horizontally according to the x-coordinate.
• After establishing your x position, move vertically based on the y-coordinate.

For example, to plot the point A(4, -1), begin at (0,0), move 4 units to the right (positive x direction), then 1 unit down (negative y direction). You’ll find point A in the lower right section of the plane.
It's important to note that the coordinate values determine the direction and distance in each step.

Quadrants

The coordinate plane is divided into four sections, known as quadrants. These quadrants are defined by the positive and negative directions of the x and y axes.
Here's what you need to know about each quadrant:

• First Quadrant: Both x and y coordinates are positive.
• Second Quadrant: x is negative, y is positive.
• Third Quadrant: Both x and y are negative.
• Fourth Quadrant: x is positive, y is negative.

For point A(4, -1), it lies in the fourth quadrant due to the positive x-coordinate (4) and negative y-coordinate (-1). Understanding quadrants helps in quickly estimating the general location of points before fine-tuning their exact positions.