/*! 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 77 Use the Midpoint Formula three t... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 77

Use the Midpoint Formula three times to find the three points that divide the line segment joining \( (x_1, y_1) \) and \( (x_2, y_2) \) into four parts.

Short Answer

Expert verified
The three points that divide the line segment into four parts are \(((3x_1 + x_2) / 4, (3y_1 + y_2) / 4\), \((x_1 + x_2) / 2, (y_1 + y_2) / 2\), and \((x_1 + 3x_2) / 4, (y_1+ 3y_2) / 4\).

Step by step solution

01

Finding the First Point

First, to find the point that divides the line segment 1/4 of the way, take the average of x and y coordinates in the ratio 3:1. It means, the x-coordinate is \((3x_1 + x_2) / 4\) and the y-coordinate is \((3y_1 + y_2) / 4\)
02

Finding the Second (Mid) Point

The second point, which is halfway along the line segment, is obtained by using the regular Midpoint Formula \((x_1 + x_2) / 2\) and \((y_1 + y_2) / 2\) for x and y-coordinate respectively.
03

Finding the Third Point

The third point, which is 3/4 of the way along the line segment, is found by taking the average of x and y coordinates in the ratio 1:3. So the x-coordinate is \((x_1 + 3x_2) / 4\) and the y-coordinate is \((y_1+ 3y_2) / 4\)

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!

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

CAPSTONE The prices of three sizes of pizza at a pizza shop are as follows. 9-inch: \(\$8.78\), 12-inch: \(\$11.78\), 15-inch: \(\$14.18\) You would expect that the price of a certain size of pizza would be directly proportional to its surface area. Is that the case for this pizza shop? If not, which size of pizza is the best buy?

In Exercises 63-76, determine whether the function has an inverse function. If it does, find the inverse function. \(p(x) = -4\)

HOURLY WAGE Your wage is \(\$10.00\) per hour plus \(\$0.75\) for each unit produced per hour. So, your hourly wage \(y\) in terms of the number of units produced \(x\) is \(y = 10 + 0.75x\). (a) Find the inverse function. What does each variable represent in the inverse function? (b) Determine the number of units produced when your hourly wage is \(\$24.25\).

SPORTS The lengths (in feet) of the winning men's discus throws in the Olympics from 1920 through 2008 are listed below. (Source: International Olympic Committee) 1920 146.6 1924 151.3 1928 155.3 1932 162.3 1936 165.6 1948 173.2 1952 180.5 1956 184.9 1960 194.2 1964 200.1 1968 212.5 1972 211.3 1976 221.5 1980 218.7 1984 218.5 1988 225.8 1992 213.7 1996 227.7 2000 227.3 2004 229.3 2008 225.8 (a) Sketch a scatter plot of the data. Let \(y\) represent the length of the winning discus throw (in feet) and let \(t=20\) represent 1920. (b) Use a straightedge to sketch the best-fitting line through the points and find an equation of the line. (c) Use the \(regression\) feature of a graphing utility to find the least squares regression line that fits the data. (d) Compare the linear model you found in part (b) with the linear model given by the graphing utility in part (c). (e) Use the models from parts (b) and (c) to estimate the winning men's discus throw in the year 2012.

THINK ABOUT IT In Exercises 77-86, restrict the domain of the function \(f\) so that the function is one-to-one and has an inverse function. Then find the inverse function \(f^{-1}\). State the domains and ranges of \(f\) and \(f^{-1}\). Explain your results. (There are many correct answers.) \(f(x) = (x-2)^2\)
See all solutions

Recommended explanations on Math Textbooks

Decision Maths

Read Explanation

Geometry

Read Explanation

Applied Mathematics

Read Explanation

Logic and Functions

Read Explanation

Statistics

Read Explanation

Probability and 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.