Problem 60 - Algebra 2

Question

Graph each set of ordered pairs on a coordinate plane. \(\\{(-3,3),(1,3),(4,2),(-1,-5)\\}\)

Step-by-Step Solution

Answer

Plot the points (-3,3), (1,3), (4,2), and (-1,-5) on the coordinate plane.

Step 1: Understanding Ordered Pairs

Each ordered pair represents a point on the coordinate plane. The first number in the pair is the x-coordinate (horizontal position) and the second number is the y-coordinate (vertical position).

Step 2: Plot the First Point (-3,3)

Start at the origin point (0,0). Move 3 units to the left along the x-axis, as the x-coordinate is -3. Then, move 3 units up along the y-axis to reach the y-coordinate of 3. Plot the point (-3,3).

Step 3: Plot the Second Point (1,3)

From the origin, move 1 unit to the right along the x-axis (x = 1) and then move 3 units up along the y-axis to the y-coordinate of 3. Plot the point (1,3).

Step 4: Plot the Third Point (4,2)

Start at the origin again, move 4 units to the right along the x-axis (x = 4), and then move 2 units up along the y-axis. Plot the point (4,2).

Step 5: Plot the Fourth Point (-1,-5)

From the origin, move 1 unit to the left along the x-axis (x = -1), then move 5 units down along the y-axis to reach the y-coordinate of -5. Plot the point (-1,-5).

Step 6: Verify the Plotting

Go through each plotted point to confirm their accuracy. Ensure that each point corresponds exactly to its respective ordered pair in the original set.

Key Concepts

Ordered Pairs

In the world of coordinate geometry, ordered pairs are foundational.
Each ordered pair consists of two numbers written in a specific order within parentheses, like \((-3,3)\).
The first number is known as the x-coordinate, which tells you how far to move horizontally.

• If it's a positive number, you move to the right of the origin.
• If it's negative, you go to the left.

The second number in the pair is the y-coordinate, indicating your vertical movement.
When it's positive, you climb upwards.
If it's negative, you head downwards.
By understanding these numbers, one can navigate the coordinate plane efficiently.

Plotting Points

Plotting points on a coordinate plane is a lot like playing a game where you navigate using directions.
Once you've interpreted an ordered pair, your task is to place the dot at the right location.

• Start from the origin, which is where the x and y-axis intersect, at point \((0,0)\).
• Follow the x-coordinate's instruction to move left or right.
• Next, follow the y-coordinate to move up or down.

It's essential to move horizontally first, and then vertically. This system ensures that each point finds its exact spot on the graph.

X-axis and Y-axis

Think of the x-axis and y-axis as the grid's backbone.
The x-axis is the horizontal line stretching left and right across the plane.

• This axis is like an endless number line, with positive increasing values going to the right and negative values spreading to the left.

Perpendicular to it is the y-axis, which runs up and down.

• The y-axis has positive values extending upwards and negative values descending below the origin.

These axes divide the plane into four quadrants, guiding us on where to plot ordered pairs and helping us understand their positions relative to the origin.

Graphing Points

Graphing points is about neatly placing various ordered pairs onto the intricate web created by the x and y axes.
Doing this visually represents relationships between numbers or data points.
When the points are correctly plotted, you might notice forming patterns or lines.

• Each point is marked where its x-coordinate and y-coordinate meet on the grid.
• Consistently graphing points helps in not only learning geometric concepts but also in portraying real-world data.

Regular practice of this skill proves invaluable in many fields, such as mathematics, physics, and even economics, as it allows for a visual understanding of potentially complex datasets.