/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 4 Fill in the blanks. Finding th... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 4

Fill in the blanks. Finding the average values of the representative coordinates of the two endpoints of a line segment in a coordinate plane is also known as using the _______ _______.

Short Answer

Expert verified
The correct term to fill in the blanks is 'Midpoint Formula'.

Step by step solution

01

Understanding the concept

Recognize the problem is referring to finding the midpoint of a line segment in a plane. To find the midpoint, the average values of the X and Y coordinates of the segment's endpoints are calculated.
02

Filling in the blanks

The description given fits the definition of the 'Midpoint Formula'. This formula locates the point that is equidistant from both endpoints of the line segment. Thus, the blanks should be filled with 'Midpoint Formula'.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

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

Coordinate Plane
Imagine a flat surface with two lines intersecting at a right angle. These lines are called axes.
The horizontal line is the x-axis and the vertical line is the y-axis.
This setup is known as the coordinate plane.

Each point on this plane can be described using a pair of numbers called coordinates.
  • The first number shows how far along the point is on the x-axis.
  • The second number shows the distance along the y-axis.
This grid helps us to better visualize and solve mathematical problems.
It acts like a map for finding points, lines, and shapes. By using the Midpoint Formula on the coordinate plane, we can find the center of a line segment with ease.
Average Values
Taking the average is a simple way to find the center between two numbers.
To find an average, you add up the numbers and divide by how many there are.

This concept is a key part of the Midpoint Formula.
  • It helps find the central point by averaging the x-coordinates and y-coordinates of endpoints.
  • This method locates a precise midpoint on a line segment.
By calculating these averages, we get one single pair of coordinates.
It鈥檚 like finding the middle ground or the exact center point between two locations on a map.
Line Segment
A line segment is a part of a line.
It has two endpoints and includes every point in between them.
Unlike a line, it does not stretch infinitely in either direction.

In the context of the coordinate plane, a line segment is specified by its two endpoints.
  • Each endpoint has its own set of coordinates.
  • The segment is the shortest path between them.
Understanding line segments is important for locating midpoints.
The segment can be visualized as a straight path or connection from one endpoint to another. This understanding is crucial when applying the Midpoint Formula.
Endpoint Coordinates
Endpoints are the two points that mark the boundary of a line segment.
Each endpoint is identified by its coordinates on the coordinate plane.

For example, endpoints might be labeled as \((x_1, y_1)\) and \((x_2, y_2)\).
  • These coordinates mark specific points on a horizontal and vertical scale.
  • They provide reference positions for using calculations like the Midpoint Formula.
By taking the average of these coordinates, the exact midpoint of the line segment is determined.
This understanding of endpoints helps tell us where a line begins and ends. Knowing their coordinates is the first step in applying mathematical formulas on a coordinate plane.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Given $$f(x)=x^{2}$$ is \(f\) the independent variable? Why or why not?

The work \(W\) done when lifting an object varies jointly with the object's mass \(m\) and the height \(h\) that the object is lifted. The work done when a 120 -kilogram object is lifted 1.8 meters is 2116.8 joules. How much work is done when lifting a 100 -kilogram object 1.5 meters?

The table shows the monthly revenue \(y\) (in thousands of dollars) of a landscaping business for each month of the year \(2013,\) with \(x=1\) representing January. $$\begin{array}{|c|c|}\hline \text { Month, \(x\) } & \text { Revenue, \(y\) } \\\\\hline 1 & 5.2 \\\2 & 5.6 \\\3 & 6.6 \\ 4 & 8.3 \\\5 & 11.5 \\\6 & 15.8 \\\7 & 12.8 \\\8 & 10.1 \\\9 & 8.6 \\\10 & 6.9 \\\11 & 4.5 \\\12 & 2.7 \\\\\hline \end{array}$$ A mathematical model that represents these data is \(f(x)=\left\\{\begin{array}{l}-1.97 x+26.3 \\ 0.505 x^{2}-1.47 x+6.3\end{array}\right.\) (a) Use a graphing utility to graph the model. What is the domain of each part of the piecewise-defined function? How can you tell? Explain your reasoning. (b) Find \(f(5)\) and \(f(11),\) and interpret your results in the context of the problem. (c) How do the values obtained from the model in part (a) compare with the actual data values?

During a nine-hour snowstorm, it snows at a rate of 1 inch per hour for the first 2 hours, at a rate of 2 inches per hour for the next 6 hours, and at a rate of 0.5 inch per hour for the final hour. Write and graph a piecewise- defined function that gives the depth of the snow during the snowstorm. How many inches of snow accumulated from the storm?

Write the area \(A\) of a square as a function of its perimeter \(P\).
See all solutions

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Read Explanation

Probability and Statistics

Read Explanation

Discrete Mathematics

Read Explanation

Logic and Functions

Read Explanation

Geometry

Read Explanation

Statistics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.