Problem 50 - Algebra 1: Concepts and Skills

Question

Plot and label the ordered pairs in a coordinate plane. $$ A(1,4), B(-2,-1), C(3,-1) $$

Step-by-Step Solution

Answer

The points A(1,4), B(-2,-1), and C(3,-1) have been plotted and labelled correctly on the coordinate plane.

Step 1: Understand each ordered pair

The ordered pairs are A(1,4), B(-2,-1), C(3,-1) meaning that for point A, the x-coordinate is 1 and the y-coordinate is 4. This is the case for each point.

Step 2: Begin plot with point A

Point A can be plotted on the coordinate plane by moving one unit to the right from the origin (since x=1) and then 4 units up (since y=4). Mark this point as point A.

Step 3: Continue with point B

Point B can be plotted by moving 2 units left from the origin (since x=-2) and then 1 unit down (since y=-1). Mark this point as point B.

Step 4: Plot point C

Plot point C by moving 3 units to the right from the origin (since x=3) and then one unit down (since y=-1). Mark this point as C.

Step 5: Label each plotted point

Label each point as per its given name (A, B, or C)

Key Concepts

Ordered Pairs

In the world of the coordinate plane, ordered pairs play a fundamental role in pinpointing exact locations. An ordered pair is composed of two numbers, encapsulated within parentheses, such as \((x, y)\). These numbers represent positions on the coordinate plane, with \(x\) indicating the horizontal position and \(y\) depicting the vertical position. This format allows us to precisely specify any point's location on the plane.

To make it easier:

• The first number in the pair is the x-coordinate.
• The second number is the y-coordinate.

For example, looking at point A(1,4), the coordinates suggest moving right one unit along the x-axis and up four units on the y-axis from the origin. Understanding this format ensures you can accurately plot any point you encounter.

Plotting Points

Plotting points on a coordinate plane is a practical application of ordered pairs. The process involves two main steps for each point: understanding the movement along the x-axis and then the y-axis. Let's break it down:

• Start at the Origin: This is the point (0,0) where both axes intersect.
• Move Along the X-Axis: Depending on the x-coordinate, move right for positive values and left for negative values.
• Move Along the Y-Axis: From your position on the x-axis, move up for positive y-values and down for negative y-values.
• Mark the Point: Once you reach the designated location, mark the point clearly and label it as specified.

For instance, to plot point B, given by B(-2,-1), start at the origin, move two units left and one unit down, and mark it as B. Repeat similar steps for other points to visualize data.

Coordinate System

The coordinate system is a method used to define and locate points on a plane using ordered pairs. This system consists of two infinite, perpendicular lines called axes:

• The Horizontal Axis: Known as the x-axis, it runs left to right.
• The Vertical Axis: Known as the y-axis, it runs up and down.

Where these axes intersect is the origin (0,0). From the origin, any point's position can be described using an ordered pair. The plane is divided into four sections known as quadrants:

1. **First Quadrant**: Both x and y are positive. 2. **Second Quadrant**: x is negative, y is positive. 3. **Third Quadrant**: Both x and y are negative. 4. **Fourth Quadrant**: x is positive, y is negative.
Understanding the layout of the coordinate system helps in visualizing mathematical concepts and solving problems like those in the given exercise.