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Chapter 2: Problem 2

Fill in the blanks. In the ordered pair \((22,29),\) the -coordinate is 29

Short Answer

Expert verified
In the ordered pair \((22,29)\), the y-coordinate is 29.

Step by step solution

01

Understand Ordered Pairs

Ordered pairs are written in the form \((x, y)\), where the first number represents the x-coordinate, and the second number represents the y-coordinate. We need to fill in the missing information in the context of coordinates.
02

Identify the Given Ordered Pair

We are given the ordered pair \((22, 29)\). Here, 22 is the first number, which corresponds to the x-coordinate, and 29 is the second number, which corresponds to the y-coordinate.
03

Determine Which Coordinate is Being Asked

The problem asks us to find out which coordinate corresponds to the number 29 in the ordered pair \((22, 29)\). From the format of ordered pairs \((x, y)\), we know that 29 is the y-coordinate.
04

Fill in the Blank

Since 29 is the second number in the ordered pair and represents the y-coordinate, we fill in the blank with 'y'.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Understanding Coordinates
Coordinates are fundamental in the field of mathematics and are used for positioning points on a plane. These points are usually represented in pairs, called ordered pairs, which take the form \((x, y)\). Here:
  • The x-coordinate tells us how far the point is along the horizontal axis.
  • The y-coordinate tells us how far the point is up or down the vertical axis.
Coordinates let us pinpoint the exact location of a point. Think of a graph like a city map, where each coordinate is like a street address. Every point on the map needs both an x and a y value to specify its unique location. Having a good grasp of how coordinates work is crucial for solving many mathematical problems involving graphs or geometric shapes.
Exploring the X-Coordinate
The x-coordinate, also known as the abscissa, represents the position of a point relative to the horizontal axis. When you look at the ordered pair \((x, y)\), the x-coordinate is the first number:
  • In a coordinate pair \((22, 29)\), 22 is the x-coordinate.
  • The x-axis runs horizontally like the horizon, indicating movement to the left or right from the origin.
The x-coordinate tells you how far to move right or left, starting from the origin \((0,0)\), which is the center point of a typical Cartesian plane. If the x-coordinate is positive, you move right. If it's negative, you move left. Understanding the x-coordinate is essential for plotting points and understanding linear equations on a graph.
The Role of the Y-Coordinate
The y-coordinate, known as the ordinate, determines the vertical position of a point on a graph. It is the second number in the ordered pair \((x, y)\):
  • In the pair \((22, 29)\), 29 is the y-coordinate.
  • The y-axis runs vertically, like a tree, indicating movement up or down from the origin.
To find the y-coordinate, you start at the origin and move up if the number is positive, or down if it is negative. The y-coordinate is key for understanding how high or low a point is on the graph. When plotting points or interpreting graphical data, the y-coordinate helps us determine vertical positioning and is critical for drawing accurate conclusions from data presented on graphs.

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