Problem 339 Plot and label these points: (... [FREE SOLUTION]

91影视

Prealgebra

Lynn Marecek, MaryAnne Anthony-Smith

$Math Studyset 91影视 Explanations$ Math

2016 Edition

Chapter 11: Problem 339

Plot and label these points: (a) $(2,5)$ (b) $(-1,-3)$ (c) $(-4,0)$ (d) $(3,-5)$ (e) $(-2,1)$

Short Answer

Expert verified

Plot and label points (2, 5), (-1, -3), (-4, 0), (3, -5), and (-2, 1) on the coordinate system.

Step by step solution

Understand the Coordinate System

The coordinate system consists of two axes: the x-axis (horizontal) and the y-axis (vertical). Each point is given as $x, y$, where $x$ represents the horizontal position and $y$ represents the vertical position.

Plot Point (2, 5)

Find x = 2 on the x-axis. Then, from this point, move vertically to y = 5. Mark this point and label it as (2, 5).

Plot Point (-1, -3)

Find x = -1 on the x-axis. Then, move vertically to y = -3. Mark this point and label it as (-1, -3).

Plot Point (-4, 0)

Find x = -4 on the x-axis. Since y = 0, this point lies exactly on the x-axis. Mark this point and label it as (-4, 0).

Plot Point (3, -5)

Find x = 3 on the x-axis. Move vertically to y = -5. Mark this point and label it as (3, -5).

Plot Point (-2, 1)

Find x = -2 on the x-axis. Then, move vertically to y = 1. Mark this point and label it as (-2, 1).

Review the Points

Ensure all points have been accurately placed on the coordinate system and correctly labeled. The points should be: (2, 5), (-1, -3), (-4, 0), (3, -5), (-2, 1).

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Key Concepts

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

x-axis and y-axis

The coordinate system is a fascinating tool that helps us locate points on a plane using two perpendicular lines: the x-axis and the y-axis. The x-axis runs horizontally, while the y-axis runs vertically. The point where these two axes intersect is called the origin, marked as $0, 0$. Each point in this system is represented by a pair of numbers: $x, y$. The x-value tells us how far to move horizontally from the origin, and the y-value shows how far to move vertically. Understanding the x-axis and y-axis is crucial because it forms the foundation of plotting points accurately.

coordinate system plotting

Plotting points in a coordinate system involves using the x and y values to locate a specific point on the plane. Let's break down the steps:

Identify the x-value of the point and find its position on the x-axis.
From there, move vertically to the y-value on the y-axis.
Mark the spot where the x and y coordinates meet, this is your point.

Practice makes perfect. For instance, to plot the point $2, 5$, start at the origin. Move 2 units to the right along the x-axis, then 5 units up along the y-axis. Mark that spot and label it (2, 5). Follow a similar process for other points, like $(-1,-3)$ or $(-4,0)$. Each movement on the grid helps you visualize the relationships between different points.

labeling points

Once you plot a point on the coordinate system, the next step is to label it. Labeling points ensures that anyone reading your graph understands the specific coordinates of each point. It's essentially providing a name tag for each plotted point.

First, mark the point clearly on the graph.
Write the coordinates next to the point in the format $x, y$.

For instance, after plotting the point $(3, -5)$, write $(3, -5)$ right next to the marked location. This practice is particularly useful when dealing with multiple points, as it avoids confusion and provides clarity. Accurate labeling is crucial in education, science, and many other fields where precise data representation is necessary.

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91影视

Plot and label these points: (a) \((2,5)\) (b) \((-1,-3)\) (c) \((-4,0)\) (d) \((3,-5)\) (e) \((-2,1)\)

Short Answer

Step by step solution

Understand the Coordinate System

Plot Point (2, 5)

Plot Point (-1, -3)

Plot Point (-4, 0)

Plot Point (3, -5)

Plot Point (-2, 1)

Review the Points

Key Concepts

x-axis and y-axis

coordinate system plotting

labeling points

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