/*! 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 32 (a) plot the points, (b) find th... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 32

(a) plot the points, (b) find the distance between the points, and (c) find the midpoint of the line segment joining the points. $$(1,12),(6,0)$$

Short Answer

Expert verified
The plotted points are A(1,12) and B(6,0). The distance between the points is 13. The midpoint of the line segment joining the points is M(3.5,6).

Step by step solution

01

Plotting The Points

To plot the points, mark the points on the graph where \(x=1, y=12\) and \(x=6, y=0\). This will correspond to points \(A(1,12)\) and \(B(6,0)\).
02

Calculate The Distance

Use the distance formula, which is \(\sqrt{((x_2-x_1)^2+(y_2-y_1)^2)}\) to find the distance between \(A(1,12)\) and \(B(6,0)\). Substituting the values into the formula, we get \(\sqrt{((6-1)^2+(0-12)^2)} = \sqrt{(25+144)} = \sqrt{169} = 13\). So, the distance between the points is 13.
03

Find The Midpoint

The midpoint formula is \((\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})\). Substituting the values from points \(A(1,12)\) and \(B(6,0)\), we get \((\frac{1+6}{2}, \frac{12+0}{2}) = (3.5, 6)\). Therefore, the midpoint of the line segment joining the points is \(M(3.5,6)\).

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

Match the data with one of the following functions $$f(x)=c x, g(x)=c x^{2}, h(x)=c \sqrt{|x|}, \quad \text {and} \quad r(x)=\frac{c}{x}$$ and determine the value of the constant \(c\) that will make the function fit the data in the table. $$\begin{array}{|c|c|c|c|c|c|}\hline x & -4 & -1 & 0 & 1 & 4 \\\\\hline y & -1 & -\frac{1}{4} & 0 & \frac{1}{4} & 1 \\\\\hline\end{array}$$

Find the difference quotient and simplify your Answer: $$f(x)=x^{2 / 3}+1, \quad \frac{f(x)-f(8)}{x-8}, \quad x \neq 8$$

Find a mathematical model that represents the statement. (Determine the constant of proportionality.) \(v\) varies jointly as \(p\) and \(q\) and inversely as the square of \(s .(v=1.5 \text { when } p=4.1, q=6.3, \text { and } s=1.2 .)\)

Find the difference quotient and simplify your Answer: $$f(x)=4 x^{2}-2 x, \quad \frac{f(x+h)-f(x)}{h}, \quad h \neq 0$$

Find the difference quotient and simplify your Answer: $$g(x)=\frac{1}{x^{2}}, \quad \frac{g(x)-g(3)}{x-3}, \quad x \neq 3$$
See all solutions

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Read Explanation

Mechanics Maths

Read Explanation

Probability and Statistics

Read Explanation

Applied Mathematics

Read Explanation

Decision Maths

Read Explanation

Logic and Functions

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.