Problem 49 Plot and label each point in a r... [FREE SOLUTION]

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Beginning Algebra

Margaret L. Lial, John Hornsby

$Math Studyset 91影视 Explanations$ Math

11 Edition

Chapter 3: Problem 49

Plot and label each point in a rectangular coordinate system. $$ (-4,2) $$

Short Answer

Expert verified

Plot the point $(-4,2)$ by moving 4 units left on the x-axis and 2 units up on the y-axis, then label it.

Step by step solution

- Identify the Coordinates

The given point is $(-4,2)$ where $x=-4$ and $y=2$.

- Draw the Coordinate Axes

Draw the horizontal x-axis and the vertical y-axis on a grid. Label the axes with numbers increasing from zero outward in both positive and negative directions.

- Locate the x-coordinate

Move horizontally along the x-axis to $-4$. This is 4 units to the left of the origin, $(0,0)$.

- Locate the y-coordinate

From $-4$ on the x-axis, move vertically to $+2$. This is 2 units up from the x-axis.

- Plot and Label the Point

Mark the point at $(-4,2)$ on the grid and label it as such.

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Key Concepts

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

rectangular coordinate system

Understanding the rectangular coordinate system is fundamental in math. This system helps us locate points on a plane using two perpendicular lines called the x-axis and y-axis.
The x-axis runs horizontally and the y-axis runs vertically.
They intersect at the origin, $ (0, 0) $, which is the center of the coordinate system.
The plane is divided into four quadrants to help plot points:

Quadrant I: Top-right, where both x and y are positive
Quadrant II: Top-left, where x is negative and y is positive
Quadrant III: Bottom-left, where both x and y are negative
Quadrant IV: Bottom-right, where x is positive and y is negative

Knowing which quadrant a point falls into is useful when plotting points.

plotting points

Plotting points in the rectangular coordinate system involves identifying coordinates and placing a dot at the correct position.
Coordinates are given as $ (x, y) $. The first number is the x-coordinate, and the second is the y-coordinate.
To plot a point, follow these steps:

Locate the x-coordinate on the x-axis
From that point, move vertically to find the corresponding y-coordinate
Mark the point where the two coordinates meet

This method allows you to accurately place any point on a grid.

coordinate axes

The coordinate axes are critical for plotting points.
The x-axis and y-axis divide the plane into four quadrants and provide a reference for locating points.

x-axis: The horizontal line where y = 0
y-axis: The vertical line where x = 0

Both axes have positive and negative sides:

Positive x-axis extends to the right
Negative x-axis extends to the left
Positive y-axis extends upward
Negative y-axis extends downward

Labeling these axes with numbers helps in identifying exact positions.

labeled points

Labeling points ensures clarity when multiple points are plotted.
Each point has a unique coordinate pair, like $ (-4, 2) $.
Here, $ -4 $ on the x-axis and $ 2 $ on the y-axis help mark the exact spot.
After plotting a point, writing its coordinates next to it helps distinguish it from others.
For example, plotting $ (-4, 2) $ means marking $ -4 $ horizontally and moving 2 units up to mark the point $ (-4, 2) $ on the grid.
This practice helps in visualizing and analyzing multiple points on a single plot.

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91影视

Plot and label each point in a rectangular coordinate system. $$ (-4,2) $$

Short Answer

Step by step solution

- Identify the Coordinates

- Draw the Coordinate Axes

- Locate the x-coordinate

- Locate the y-coordinate

- Plot and Label the Point

Key Concepts

rectangular coordinate system

plotting points

coordinate axes

labeled points

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