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Chapter 7: Problem 8

Plot the given point in a rectangular coordinate system. \((3,-2)\)

Short Answer

Expert verified
Starting from the origin, move 3 units to the right along the x-axis, then move 2 units down along the y-axis. Mark the point \((3,-2)\).

Step by step solution

01

Understand the Cartesian Plane

In a Cartesian Plane there are two axes, the x-axis (horizontal line) and y-axis (vertical line). These axes intersect each other at a point called origin, denoted by \((0,0)\). The x-coordinate (the first number) represents the horizontal position and the y-coordinate (the second number) represents the vertical position of a point.
02

Locate the x-coordinate

Start from the origin. The x-coordinate is 3, meaning move 3 units to the right. This is because x-coordinates to the right of the origin are positive.
03

Locate the y-coordinate

From the position after step 2, the y-coordinate is -2, meaning move 2 units downwards. This is because y-coordinates below the origin are negative.
04

Plot the Point

Draw a dot at the location determined by the x and y positions. This is the point \((3,-2)\).

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Key Concepts

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

Plotting Points
Plotting points on a Cartesian coordinate system is like marking a spot on a map. Imagine a graph with two lines that cross at the center: the horizontal line (x-axis) and the vertical line (y-axis). Each point is represented by a pair of numbers called coordinates, such as \((3, -2)\), which help you find its exact location. The **first number** is the x-coordinate, which tells you how far to move horizontally. The **second number** is the y-coordinate, guiding your vertical movement.
To plot the point \((3, -2)\), start at the origin \((0,0)\). Move 3 units to the right and then 2 units down. You'll find your spot on the grid, where you can mark it to make it official!
Remember:
  • The order does matter. Always check which number is the x-coordinate and which is the y-coordinate.
  • Positive numbers move you right or up, while negative numbers move you left or down.
x-axis and y-axis
The x-axis and y-axis are the backbone of the Cartesian coordinate system. They divide the plane into four sections, called quadrants. The **x-axis** is the horizontal line that runs left to right. It helps in finding the horizontal position of a point.
The **y-axis** runs vertically from top to bottom. It determines the vertical position of a point.
Here are a few important things about the axes:
  • The axes intersect at the **origin** \((0,0)\), which is the starting point for any movement on the graph.
  • The **x-axis** is like the horizon; if a coordinate is on it, then its y-value is 0.
  • The **y-axis** is like a towering line; points along it have an x-value of 0.
Understanding these axes helps you navigate the plane easily, so you can plot or read points without getting lost.
Negative and Positive Coordinates
Coordinates can be positive or negative, which tells you in which direction to move from the origin. Positive coordinates are like giving directions to move right and up. **For example:** In the point \((3, -2)\):
  • The **x-coordinate, 3,** means go right because it's positive.
  • The **y-coordinate, -2,** means go down because it's negative.
It's like a treasure map where positive values guide you towards one treasure, and negative values point to another.

A quick tip:
  • Positive x values are to the right of the y-axis, while negative x values go to the left.
  • For y-values, positives are above the x-axis, and negatives are below.
Getting the hang of positive and negative coordinates lets you navigate the graph with ease, ensuring you plot every point accurately.

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Most popular questions from this chapter

Graph each linear inequality. \(y>\frac{1}{3} x\)

Without graphing, Determine if each system has no solution or infinitely many solutions. \(\left\\{\begin{array}{l}3 x+y \leq 9 \\ 3 x+y \geq 9\end{array}\right.\)

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