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Chapter 2: Problem 27

In which quadrant or on which axis is each point located? \((160,2)\)

Short Answer

Expert verified
(160, 2) is in the first quadrant.

Step by step solution

01

Identify the Coordinates

Identify the given coordinates. The point provided is \(160, 2\)
02

Determine the Sign of Each Coordinate

Evaluate the signs of each coordinate. Here, \(160\) is positive and \(2\) is also positive.
03

Determine the Quadrant

Recall that a point \( (x, y) \) lies in the first quadrant if both \(x\) and \(y\) are positive. Since \(160 > 0\) and \(2 > 0\), the point \( (160, 2) \) is in the first quadrant.

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Key Concepts

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

Coordinate Plane
The coordinate plane is a fundamental concept in geometry and algebra. It allows us to visualize and plot points in a two-dimensional space. The plane consists of two perpendicular lines called axes.
  • X-Axis: This is the horizontal line. It's typically drawn left to right.
  • Y-Axis: This is the vertical line. It's typically drawn bottom to top.
These axes intersect at a point called the origin, which has coordinates \text{\((0,0)\)}. Every other point on the plane is defined by its distance from the origin along the x-axis and y-axis.
The coordinate plane allows for a precise representation of locations and is used extensively in mathematics to graph functions, equations, and inequalities.
Quadrants
The coordinate plane is divided into four sections called quadrants. Each of these quadrants has distinct characteristics:
  • First Quadrant: Located in the upper-right section. Here, both x and y coordinates are positive.
  • Second Quadrant: Located in the upper-left section. Here, x coordinates are negative, and y coordinates are positive.
  • Third Quadrant: Located in the lower-left section. Both x and y coordinates are negative.
  • Fourth Quadrant: Located in the lower-right section. x coordinates are positive, and y coordinates are negative.
Each point on the plane falls into one of these quadrants or on one of the axes. For example, in our exercise, the point \((160, 2)\) is in the First Quadrant, since both coordinates are positive.
Signs of Coordinates
The signs of the coordinates tell us in which quadrant or on which axis a point lies. Let's break it down:
  • Positive x and y: The point is in the First Quadrant.
  • Negative x and positive y: The point is in the Second Quadrant.
  • Negative x and y: The point is in the Third Quadrant.
  • Positive x and negative y: The point is in the Fourth Quadrant.
  • x is zero: The point lies on the y-axis.
  • y is zero: The point lies on the x-axis.
Understanding these signs helps us quickly locate points on the coordinate plane. For example, in the given exercise, since both 160 and 2 are positive, the point \text{\((160, 2)\)} is in the First Quadrant. Remember, simply checking the signs of coordinates can immediately tell you which quadrant the point belongs to.

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Most popular questions from this chapter

Use a graph to estimate the solution in each of the following. Be sure to use graph paper and a straightedge. Kay's Auto Village charges \(\$ 50\) for a road call plus \(\$ 15\) for each 15 -min unit of time. Estimate the time required for a road call that cost \(\$ 140\).

Use a commutative law to write an expression equivalent to $7+t

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Find the intercepts. Then graph by using the intercepts, if possible, and a third point as a check. $$ 0.2 y-1.1 x=6.6 $$

Explain the difference between finding \(f(0)\) and finding the input \(x\) for which \(f(x)=0\)
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