Problem 42 In which quadrant or on which ax... [FREE SOLUTION]

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Chapter 3: Problem 42

In which quadrant or on which axis is each point located? $$ (-1,-4) $$

Short Answer

Expert verified

Quadrant III

Step by step solution

Identify the x-coordinate

The x-coordinate of the point is the first number in the pair. For the point $(-1, -4)$, the x-coordinate is $-1$.

Identify the y-coordinate

The y-coordinate of the point is the second number in the pair. For the point $(-1, -4)$, the y-coordinate is $-4$.

Determine the signs of the coordinates

Since the x-coordinate $-1$ is negative and the y-coordinate $-4$ is also negative, both coordinates are negative.

Locate the quadrant based on the signs

Points with both negative x and y coordinates are located in Quadrant III.

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Key Concepts

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

quadrants

In coordinate geometry, the plane is divided into four quadrants. Each quadrant is defined by the signs of the x-coordinates and y-coordinates of a point.

The quadrants are:

Quadrant I: Both x and y coordinates are positive
Quadrant II: x coordinate is negative and y coordinate is positive
Quadrant III: Both x and y coordinates are negative
Quadrant IV: x coordinate is positive and y coordinate is negative

Knowing which quadrant a point lies in helps us understand its position better.

x-coordinate

The x-coordinate of a point gives the horizontal position of the point on the coordinate plane. It is the first value in an ordered pair $(x, y)$. For example, in the point $(-1, -4)$, the x-coordinate is $-1$.

If the x-coordinate is positive, the point lies to the right of the y-axis. If the x-coordinate is negative, the point lies to the left of the y-axis. This helps in determining which quadrant the point may be located in.

y-coordinate

The y-coordinate of a point gives the vertical position of the point on the coordinate plane. It is the second value in an ordered pair $(x, y)$. For the point $(-1, -4)$, the y-coordinate is $-4$.

If the y-coordinate is positive, the point is above the x-axis. If the y-coordinate is negative, the point is below the x-axis. The y-coordinate, together with the x-coordinate, determines the exact location of the point in the coordinate plane.

negative coordinates

When both coordinates of a point are negative, the point is located in Quadrant III. For instance, in the point $(-1, -4)$, both the x-coordinate and y-coordinate are negative. Therefore, this point is situated in Quadrant III.

Negative coordinates indicate specific directional positions:

Negative x-coordinate: To the left of the y-axis
Negative y-coordinate: Below the x-axis

This concept is crucial for graphing and understanding the placement of points on the coordinate plane.

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91影视

In which quadrant or on which axis is each point located? $$ (-1,-4) $$

Short Answer

Step by step solution

Identify the x-coordinate

Identify the y-coordinate

Determine the signs of the coordinates

Locate the quadrant based on the signs

Key Concepts

quadrants

x-coordinate

y-coordinate

negative coordinates

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