Problem 33 - Prealgebra

Question

Graph each ordered pair on a coordinate system. $$K(0,2)$$

Step-by-Step Solution

Answer

Plot a point 2 units up on the y-axis, at (0, 2).

Step 1: Understand the Ordered Pair

The ordered pair given is \( K(0, 2) \). This means that the point \( K \) has an \( x \)-coordinate of 0 and a \( y \)-coordinate of 2. This sets the location of the point on the coordinate system.

Step 2: Set Up the Coordinate System

Draw two perpendicular lines intersecting at right angles, which will be your axes. Label the horizontal line as the \( x \)-axis and the vertical line as the \( y \)-axis. Identify their intersection, which is the origin, marked as \( (0, 0) \).

Step 3: Locate the x-position

Using the \( x \)-coordinate of the point \( K \), which is 0, stay at the origin since the \( x \)-coordinate indicates no movement left or right along the \( x \)-axis.

Step 4: Locate the y-position

From the origin, move vertically according to the \( y \)-coordinate of the point \( K \), which is 2. Move 2 units upwards along the \( y \)-axis from the point \( (0, 0) \).

Step 5: Plot the Point

Mark the location on the graph where the two movements intersect. The point \( K(0, 2) \) should be plotted directly on the \( y \)-axis, 2 units above the origin.

Key Concepts

Understanding Ordered Pairs

In a coordinate system, an ordered pair provides a clear way to define the location of a point. An ordered pair is written in the format \(x, y\), where \(x\) represents the x-coordinate and \(y\) represents the y-coordinate. This order is essential because it tells you exactly how to move from the origin, which is located at \(0, 0\).Think of it like getting directions. First, you follow the instruction for \(x\), and then for \(y\).

• The first number indicates the horizontal movement on the x-axis.
• The second number tells you the vertical movement on the y-axis.

By using ordered pairs, you can precisely locate any point on a two-dimensional plane.

The Role of the x-coordinate

The x-coordinate is the first number in an ordered pair and tells you how far to move left or right from the origin. The x-axis runs horizontally across the graph.

• If the x-coordinate is positive, move to the right.
• If it's negative, move to the left.
• If it's zero, you stay on the vertical line of the y-axis.

For example, in the ordered pair \(K(0, 2)\), the x-coordinate is 0. This means there is no horizontal movement needed, and the point remains directly above or below the origin, depending on the y-coordinate.

Explaining the y-coordinate

The y-coordinate in an ordered pair dictates the vertical movement from the origin on the graph. It is the second number in the ordered pair and has its own role, just like the x-coordinate.

• If the y-coordinate is positive, move upwards.
• If it is negative, move downwards.
• If it is zero, remain on the x-axis line.

So in \(K(0, 2)\), the y-coordinate is 2, which means to move 2 units up from where you are after considering the x-coordinate. This helps in accurately placing the point on the coordinate plane.

Plotting Points on a Coordinate System

Plotting points on a coordinate system can initially seem tricky, but it boils down to breaking it into steps. You first need to understand the grid setup:1. Draw two perpendicular lines, with the horizontal one being the x-axis and the vertical one being the y-axis.2. Start by identifying the origin at \(0, 0\).To plot a point:

• Use the x-coordinate to find the horizontal position.
• Then, use the y-coordinate for the vertical position.

Finally, mark the spot where these coordinates lead you. For the ordered pair \(K(0, 2)\), you are starting at the origin and simply moving two units up, directly on the y-axis. Plotting this way ensures accuracy and clarity in understanding the point's exact location on the plane.