/*! 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 \(\left(x_{1}, y_{1}\right)\) and \(\left(x_{2}, y_{2}\right)\) into four parts.

Short Answer

Expert verified
The points that divide the line segment \( \left(x_{1}, y_{1}\right) \) and \( \left(x_{2}, y_{2}\right) \) into four equal parts are \( M_1 = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \), \( M_2 = \left( \frac{x_1 + \frac{x_1 + x_2}{2}}{2}, \frac{y_1 + \frac{y_1 + y_2}{2}}{2} \right) \), and \( M_3 = \left( \frac{x_2 + \frac{x_1 + x_2}{2}}{2}, \frac{y_2 + \frac{y_1 + y_2}{2}}{2} \right) \).

Step by step solution

01

Remember the Midpoint formula

The Midpoint formula for a line segment connecting two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is given by \( M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \). It calculates the geographical center point of the line.
02

Find First Midpoint

First, apply the Midpoint formula between the points \( (x_1, y_1) \) and \( (x_2, y_2) \) to get the first midpoint \( M_1 = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \). This point divides the line into two equal parts.
03

Find Second Midpoint

Then, apply the same formula again, but this time between the points \( (x_1, y_1) \) and the first Midpoint \( M_1 \) that you computed earlier, which will give you the second point \( M_2 = \left( \frac{x_1 + \frac{x_1 + x_2}{2}}{2}, \frac{y_1 + \frac{y_1 + y_2}{2}}{2} \right) \). This point further divides one half of the line segment into two equal parts.
04

Find Third Midpoint

Lastly, apply the formula between the points \( (x_2, y_2) \) and the first Midpoint \( M_1 \), which will give you the third point \( M_3 = \left( \frac{x_2 + \frac{x_1 + x_2}{2}}{2}, \frac{y_2 + \frac{y_1 + y_2}{2}}{2} \right) \). This point further divides the remaining half of the segment into two equal parts. Now, the line segment has been divided into four equal parts by the points \( M_1, M_2 \) and \( M_3 \).

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

Determine whether the function has an inverse function. If it does, find the inverse function. $$ f(x)=\sqrt{x-2} $$

When buying gasoline, you notice that 14 gallons of gasoline is approximately the same amount of gasoline as 53 liters. Use this information to find a linear model that relates liters \(y\) to gallons \(x\). Then use the model to find the numbers of liters in 5 gallons and 25 gallons.

Determine whether the variation model is of the form \(y=k x\) or \(y=k / x,\) and find \(k .\) Then write \(a\) model that relates \(y\) and \(x\). $$ \begin{array}{|c|c|c|c|c|c|} \hline x & 5 & 10 & 15 & 20 & 25 \\ \hline y & -3.5 & -7 & -10.5 & -14 & -17.5 \\ \hline \end{array} $$

Determine whether the variation model is of the form \(y=k x\) or \(y=k / x,\) and find \(k .\) Then write \(a\) model that relates \(y\) and \(x\). $$ \begin{array}{|c|c|c|c|c|c|} \hline x & 5 & 10 & 15 & 20 & 25 \\ \hline y & 24 & 12 & 8 & 6 & \frac{24}{5} \\ \hline \end{array} $$

Assume that \(y\) is directly proportional to \(x\). Use the given \(x\) -value and \(y\) -value to find a linear model that relates \(y\) and \(x\). $$ x=5, y=12 $$
See all solutions

Recommended explanations on Math Textbooks

Logic and Functions

Read Explanation

Applied Mathematics

Read Explanation

Mechanics Maths

Read Explanation

Statistics

Read Explanation

Pure Maths

Read Explanation

Theoretical and Mathematical Physics

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.