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Chapter 15: Problem 7

First coordinates are positive in quadrants ___________ and ____________.

Short Answer

Expert verified
Quadrant I and Quadrant IV

Step by step solution

01

Understand the Coordinate Plane

A coordinate plane is divided into four quadrants. Each quadrant is determined by the signs of the x (horizontal) and y (vertical) coordinates.
02

Identify the Quadrants

The quadrants are named as follows: 1. Quadrant I: Both x and y coordinates are positive.2. Quadrant II: x is negative, y is positive.3. Quadrant III: Both x and y coordinates are negative.4. Quadrant IV: x is positive, y is negative.
03

Determine Quadrants with Positive First Coordinates

Given the quadrants, the first coordinates (x-values) are positive in Quadrant I and Quadrant IV.

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Key Concepts

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

positive coordinates
In the coordinate plane, each point is defined by a pair of coordinates \(x,y\). When both coordinates are positive, the point lies in Quadrant I. However, a coordinate can also have one positive and one negative value, or both negative, depending on its location.

Positive coordinates mean the coordinates have values greater than zero. For example, (3, 2) and (4, 5) are examples of positive coordinates.

Understanding if the coordinates are positive helps in identifying which quadrant the point lies in.
x-axis
The x-axis is the horizontal line in the coordinate plane. It divides the plane into top and bottom halves.

To denote a point in the coordinate system, you use two values, (x, y). The x value shows how far along the point is on the horizontal x-axis.

Positive values of x are to the right of the origin (0, 0) while negative values are to the left. This concept is essential for locating points on the coordinate plane.
y-axis
The y-axis is the vertical line in the coordinate plane. It splits the plane into left and right halves.

In the coordinate system, the y value shows how far up or down the point is on the vertical y-axis.

Positive values of y are above the origin, while negative values are below. Understanding the y-axis's positive and negative areas helps in pinpointing a point's position in the plane.
quadrants
A coordinate plane is divided into four sections called quadrants:

  • Quadrant I: Both x and y coordinates are positive. Example: (2, 3)
  • Quadrant II: x is negative, y is positive. Example: (-2, 3)
  • Quadrant III: Both x and y coordinates are negative. Example: (-2, -3)
  • Quadrant IV: x is positive, y is negative. Example: (2, -3)
Knowing the sign of the coordinates can help you quickly determine which quadrant a point falls into.

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