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Chapter 3: Problem 48

In which quadrant or on which axis is each point located? $$ (7.5,2.9) $$

Short Answer

Expert verified
The point (7.5, 2.9) is located in the first quadrant.

Step by step solution

01

Understanding the Coordinate System

The coordinate system is divided into four quadrants. The first quadrant is in the top-right, the second quadrant is in the top-left, the third quadrant is in the bottom-left, and the fourth quadrant is in the bottom-right.
02

Analyzing the Point

The coordinates given are (7.5, 2.9). Determine the sign of each coordinate to identify the quadrant.
03

Determine the Signs

The x-coordinate is 7.5, which is positive, and the y-coordinate is 2.9, which is also positive.
04

Identify the Quadrant

Since both the x and y coordinates are positive, the point (7.5, 2.9) is located in the first quadrant.

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Key Concepts

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

Quadrants
The coordinate system is divided into four quadrants. These quadrants help to locate points on a coordinate plane easily.

The four quadrants are:
  • First Quadrant: Located in the top-right section of the plane. Both x and y coordinates are positive.
  • Second Quadrant: Found in the top-left section. Here, the x coordinate is negative while the y coordinate is positive.
  • Third Quadrant: Positioned in the bottom-left. Both x and y coordinates are negative in this region.
  • Fourth Quadrant: Located in the bottom-right. The x coordinate is positive and the y coordinate is negative.
Knowing which quadrant a point lies in helps in understanding its positional attributes and provides clarity on its values.
Coordinate Plane
A coordinate plane is a two-dimensional surface where we can plot points, lines, and curves to solve geometric problems. It consists of two main axes:
  • x-axis: The horizontal line.
  • y-axis: The vertical line.
These axes intersect at a point called the origin, which has coordinates (0,0). The coordinate plane is crucial in various fields like mathematics, physics, and engineering as it graphically represents relationships between numbers and variables.

By using the coordinate plane, you can easily see how different points relate to each other spatially.
Signs of Coordinates
Understanding the signs of coordinates is essential for correctly identifying the location of points in different quadrants. The signs of the x and y coordinates determine in which quadrant a point is located:
  • Positive x and positive y: First Quadrant.
  • Negative x and positive y: Second Quadrant.
  • Negative x and negative y: Third Quadrant.
  • Positive x and negative y: Fourth Quadrant.
When the coordinates are on the axes:
  • If one of the coordinates is zero while the other is not, the point lies on one of the axes.
  • For example, (0,5) lies on the y-axis and (4,0) lies on the x-axis.
Remember, the sign of each coordinate gives a clear indication of its position in the coordinate plane.

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