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Chapter 9: Problem 14

Determine the quadrant in which the point is located. $$(78,65)$$

Short Answer

Expert verified
Answer: The point (78, 65) is located in the first quadrant.

Step by step solution

01

Determine the coordinates of the point

The coordinates of the given point are (78, 65).
02

Analyze the x-coordinate

The x-coordinate of the point is 78, which is positive.
03

Analyze the y-coordinate

The y-coordinate of the point is 65, which is also positive.
04

Determine the quadrant

Since both the x and y coordinates are positive, the point (78, 65) 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 plane is divided into four sections, known as quadrants. These quadrants help us pinpoint the exact location of a point based on its coordinates. The quadrants are numbered from I to IV and move counterclockwise around the plane.
  • Quadrant I: Both x and y coordinates are positive.
  • Quadrant II: The x-coordinate is negative, and the y-coordinate is positive.
  • Quadrant III: Both x and y coordinates are negative.
  • Quadrant IV: The x-coordinate is positive, and the y-coordinate is negative.
Each quadrant tells us about the signs of the coordinates in that section of the plane. This can help us determine a point's position quickly.
x-coordinate
The x-coordinate tells us how far to move horizontally from the origin, which is the point (0,0). It indicates whether the direction is to the left or right on the coordinate plane.

  • A positive x-coordinate means the point lies to the right of the origin.
  • A negative x-coordinate means the point lies to the left of the origin.
Understanding the x-coordinate helps us know the horizontal position of a point, such as the 78 in (78, 65), which places it on the positive side of the x-axis.
y-coordinate
The y-coordinate helps us determine how far to move up or down from the origin. It tells us the vertical position of a point on the coordinate plane.

  • A positive y-coordinate indicates the point is above the origin.
  • A negative y-coordinate means the point is below the origin.
For example, the y-coordinate 65 in the point (78, 65) shows that the point is above the origin, further solidifying its position in the first quadrant.
Positive Coordinates
When both the x-coordinate and the y-coordinate of a point are positive, the point will be located in the first quadrant. This is because the first quadrant includes all points where both values are positive, reflecting movement to the right and upwards from the origin.

Positive coordinates, such as (78, 65), provide an easy way to visualize a point's positive horizontal and vertical location on the plane. Understanding this concept is fundamental for correctly identifying the location of points in the coordinate system.

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