Problem 4 - Algebra 1: Concepts and Skills

Question

Plot and label the ordered pairs in a coordinate plane. $$ A(4,-1), B(5,0) $$

Step-by-Step Solution

Answer

The points A(4,-1) and B(5,0) have been plotted and labeled in the Cartesian coordinate plane.

Step 1: Plot Point A

Locate the coordinates for point A on the graph. The first number in the ordered pair (4, -1) is the x-coordinate which represents a movement along the x-axis. The x-coordinate is positive, so move 4 units to the right of the origin. The second number is the y-coordinate which represents a movement up or down. The y-coordinate is negative, so move 1 unit down. Mark this spot as point A.

Step 2: Plot Point B

Next, locate the coordinates for point B (5, 0). The x-coordinate is positive, so move 5 units to the right of the origin. The y-coordinate is zero, so there's no movement up or down. Mark this spot as point B.

Step 3: Label the Points

Finally, label the points as A and B respectively. This differentiates them on the graph.

Key Concepts

Ordered Pairs

Ordered pairs are an essential concept in mathematics, especially when dealing with coordinate planes. An ordered pair is a set of two numbers written in a specific order, usually enclosed in parentheses and separated by a comma, such as \(x, y\). The importance of ordered pairs lies in their ability to precisely locate points in a two-dimensional space.

When interpreting ordered pairs in the context of a coordinate plane:

• The first number corresponds to the horizontal position, or x-coordinate.
• The second number corresponds to the vertical position, or y-coordinate.

So, if you have an ordered pair like (4, -1), it tells you to move 4 units horizontally from the origin, and then 1 unit down vertically. This method of locating a point is vital for graphing and solving various types of algebraic problems.

By understanding ordered pairs, you can effortlessly plot points and navigate the coordinate plane with precision.

X-Coordinate

The x-coordinate in an ordered pair represents the position along the x-axis, which is the horizontal axis in a coordinate plane.

Understanding the x-coordinate is simple:

• If the value is positive, you move to the right of the origin on the x-axis.
• If the value is zero, you remain at the origin when considering only the x-axis movement.
• If the value is negative, you move to the left of the origin.

For example, in the point A(4, -1), the x-coordinate 4 means that you start at the origin (0,0) and move 4 units along the x-axis in the positive direction. This movement is crucial for correctly placing the point on the plane.

Remember, the x-coordinate always comes first in an ordered pair and it dictates the horizontal positioning of any point on the coordinate plane.

Y-Coordinate

The y-coordinate is the second element in an ordered pair and signifies the position along the y-axis, which is the vertical axis of the coordinate plane.

Let's break down how to read and use the y-coordinate:

• A positive y-coordinate means moving up from the origin.
• If the y-coordinate is zero, you don't move up or down; the point is level with the x-axis.
• A negative y-coordinate indicates movement downward from the origin.

In the context of the ordered pair for point A(4, -1), the y-coordinate -1 tells you to move 1 unit down from the x-axis position. This downward movement is a key insight for understanding where your point will land on the graph.

By mastering the concept of the y-coordinate, you can accurately determine the vertical position of any point in the coordinate plane, leading to more precise graphing and analysis.