Problem 42 - Prealgebra

Question

Graph each ordered pair on a coordinate system. $$X(1,1.3)$$

Step-by-Step Solution

Answer

Plot point \((1, 1.3)\) by moving 1 unit right and 1.3 units up.

Step 1: Understand the Ordered Pair

An ordered pair is a pair of numbers used to locate a point on a coordinate plane. The first number is the x-coordinate, and the second number is the y-coordinate. In the pair \(X(1, 1.3)\), \(1\) is the x-coordinate and \(1.3\) is the y-coordinate.

Step 2: Identify the Quadrant or Axis

Since both coordinates \(1\) and \(1.3\) are positive, this point lies in the first quadrant of the coordinate plane, where both x and y values are positive.

Step 3: Plot the x-coordinate

Start at the origin \((0,0)\) on the coordinate plane. Move horizontally 1 unit to the right to reach \(x = 1\).

Step 4: Plot the y-coordinate

From \(x = 1\), move vertically 1.3 units up to position \((1, 1.3)\). Since this is a fractional value, ensure that it's positioned between the integer values 1 and 2 on the y-axis.

Step 5: Mark the Point

Once you reach \((1, 1.3)\), place a point on the coordinate plane. Label this point as \(X\).

Key Concepts

Coordinate Plane

Imagine a big sheet of graph paper. When we talk about the coordinate plane, we are referring to quite a similar concept. It's a flat surface that helps us to picture where points are in a two-dimensional space. The coordinate plane comprises two number lines: one horizontal and one vertical.

• The horizontal line is known as the x-axis.
• The vertical line is called the y-axis.
• These two axes intersect at a point we call the origin, denoted by (0,0).

The coordinate plane can be divided into four sections, called quadrants, that help identify the location of points based on their coordinates. This organization helps us solve problems involving distances, areas, and much more.

x-coordinate

The x-coordinate is the number that tells us how far left or right our point is from the origin on the coordinate plane. It’s the first number in any ordered pair like (1, 1.3). If you think of the x-axis as a line pointing east and west, the x-coordinate shows the distance you travel along this line.

• A positive x-coordinate means you move to the right of the origin.
• A negative x-coordinate means you move to the left.

For the point (1, 1.3), the x-coordinate is 1, indicating a movement 1 unit to the right from the origin along the x-axis. Taking this step is the crucial first move in plotting any point on the coordinate plane.

y-coordinate

The y-coordinate is the second number in an ordered pair and it tells us how far up or down the point is from the origin along the y-axis. It's like climbing a ladder that goes straight up or down from where you stand on the x-axis.

• A positive y-coordinate indicates movement upward.
• A negative y-coordinate indicates movement downward.

For the point (1, 1.3), the y-coordinate is 1.3. This tells us to move 1.3 units upwards from our initial x-coordinate position of 1. It's key to consider fractional coordinates like 1.3 with care, positioning your point precisely between whole numbers if necessary.

First Quadrant

The first quadrant is the area of the coordinate plane where both x and y values are positive. Think of it as the top-right section when you look at the entire plane. Points in this quadrant are located both to the right of the origin and above it. Some features of the first quadrant include:

• Any point plotted in this region has coordinates like (positive, positive), such as (1, 1.3).
• It's commonly the first region explored when learning about the coordinate plane because it's easy to visualize and comprehend.

Understanding which quadrant a point falls into helps reinforce your understanding of positive and negative values on the coordinate plane and can guide you in plotting and analyzing points effectively.