Problem 13 - Algebra 1

Question

Plot and label the ordered pairs in a coordinate plane. $$A(0,3), B(-2,-1), C(2,0)$$

Step-by-Step Solution

Answer

The points \(A(0,3)\), \(B(-2,-1)\), and \(C(2,0)\) have been plotted and labeled correctly on the coordinate plane.

Step 1: Identify Coordinates

In order to plot each point, one must identify the x-coordinate (the first number) as the position on the horizontal axis, and the y-coordinate (the second number) as the position on the vertical axis. So, \(A\) has coordinates (0,3), \(B\) has coordinates (-2,-1), and \(C\) has coordinates (2,0).

Step 2: Plot Coordinates on the Plane

Begin by plotting the x (horizontal) and y (vertical) axes. The point \(A(0,3)\) can be plotted by moving along the y-axis (upwards because it is positive) 3 spaces, since the x-coordinate is zero. For \(B(-2,-1)\), first move left 2 spaces along the x-axis (because it is negative) then down 1 space (because it is also negative). For \(C(2,0)\), move right 2 spaces along the x-axis.

Step 3: Label the points

After plotting the points, label them clearly with their respective letters on the coordinate plane next to the points.

Key Concepts

Ordered Pairs

Ordered pairs are a set of numbers that provide precise locations for points on a coordinate plane. They are written within parentheses and separated by a comma, like this:

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

Ordered pairs are fundamental in mathematics as they help identify exact positions. They offer a simple way to convey the location of your point relative to two intersecting axes: the horizontal axis (x-axis) and the vertical axis (y-axis).
For example, in the ordered pair \( (2, 3) \), 2 dictates movement along the x-axis, and 3 addresses shifts on the y-axis.

Plotting Points

Plotting points on a coordinate plane is essentially drawing the points represented by ordered pairs. The coordinate plane consists of two lines intersecting at right angles which divide it into four quadrants.
Here’s how to plot points step-by-step:

• First, locate the x-coordinate on the horizontal axis.
• Move vertically to match the y-coordinate on the vertical axis.
• Mark the spot where your coordinates meet.

Plotting is an important skill because it visually represents mathematical concepts and data. It provides an easy visual way to see the relationship and location of different points on a plane.

X-Coordinate

The x-coordinate is an integral part of an ordered pair, representing the horizontal position of a point on the coordinate plane.
It is always the first number in an ordered pair \( (x, y) \).

• If the x-coordinate is positive, you move to the right from the origin (0,0).
• If it is negative, you move to the left.

Understanding x-coordinates is crucial for correctly plotting points. They tell us how far along the x-axis we need to travel before considering vertical movement.

Y-Coordinate

The y-coordinate in an ordered pair determines the vertical position of a point on the coordinate plane.
It comes second in an ordered pair \( (x, y) \).

• A positive y-coordinate implies a movement upward from the x-axis.
• A negative y-coordinate requires you to move downward.

The y-coordinate is just as essential as the x-coordinate because it specifies how high or low a point is located relative to the horizontal x-axis. It's like the elevator direction: up or down from the ground floor (x-axis).