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Chapter 10: Problem 35

Graph each point on a coordinate plane. $$W(-2,-4)$$

Short Answer

Expert verified
Plot \((-2,-4)\) by moving 2 units left and 4 units down from the origin.

Step by step solution

01

Understand the Coordinate System

A coordinate plane has two axes: the horizontal axis called the x-axis and the vertical axis called the y-axis. Points are plotted using pairs of numbers known as coordinates, written as \((x, y)\). These indicate position in the plane.
02

Identify the Values

The given point is \(W(-2, -4)\). The first number, \(-2\), is the x-coordinate and tells us how far to move horizontally from the origin. The second number, \(-4\), is the y-coordinate and tells us how far to move vertically.
03

Plot the x-coordinate

Start at the origin \((0, 0)\) on the coordinate plane. Move left along the x-axis since the x-coordinate \(-2\) is negative. Stop at \(-2\) on the x-axis.
04

Plot the y-coordinate

From \(-2\) on the x-axis, move downward since the y-coordinate \(-4\) is negative. Stop at \(-4\) on the y-axis.
05

Mark the Point

The intersection of the line drawn from \(-2\) on the x-axis and line drawn from \(-4\) on the y-axis is the point \((-2, -4)\). Place a point here and label it with \(W\).

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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 coordinate plane is like marking locations on a map. Each point is represented by a pair of numbers known as coordinates, formatted as \((x, y)\). These coordinates serve as precise directions on where to place the point.
To plot a point correctly:
  • Start from the origin, which is the point \((0, 0)\) where the x-axis and y-axis intersect.
  • Move horizontally first according to the x-coordinate.
  • Then, move vertically according to the y-coordinate.
  • Mark the spot where your moves intersect.
If the x-coordinate is positive, move right; if it's negative, go left. Similarly, if the y-coordinate is positive, move up; if negative, go down. This systematic approach ensures that each point is plotted correctly.
x-axis and y-axis
The x-axis and y-axis form the backbone of the coordinate plane. Understanding them helps in navigating the plane effectively.

x-axis
The x-axis is the horizontal line that runs left to right. It is used to determine the horizontal position of a point. Positions along the x-axis are measured using the x-coordinate.
  • If the x-coordinate is positive, the point is on the right of the origin.
  • If negative, the point lies on the left.

y-axis
The y-axis is the vertical line that runs up and down. It is used to determine the vertical position, measured by the y-coordinate.
  • A positive y-coordinate places the point above the origin.
  • A negative y-coordinate places it below.
Together, these axes divide the plane into four quadrants and help us pinpoint exact locations.
Negative Coordinates
Negative coordinates play a crucial role in determining a point's position on a coordinate plane, especially when the point lies in different quadrants. Coordinates can be negative in either the x or y direction, or even both, which determines where you move from the origin.

  • If both coordinates are negative, like \((-2, -4)\), the point will be in the third quadrant.
  • Moving left from the origin occurs with a negative x-coordinate.
  • Moving downward occurs with a negative y-coordinate.
Understanding negative coordinates helps plot points accurately even when they鈥檙e situated in non-positive regions of the plane. This is essential for visualizing graphs that extend into different quadrants beyond the first.

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