/*! 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 35 Determine whether the given poin... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 0: Problem 35

Determine whether the given points lie on a straight line. $$ A(-3,6), B(3,3), \text { and } C(6,0) $$

Short Answer

Expert verified
The slopes between points A and B, and B and C are \(m_{AB} = -\frac{1}{2}\) and \(m_{BC} = -1\), respectively. Since they are not equal, the points A(-3, 6), B(3, 3), and C(6, 0) do not lie on a straight line.

Step by step solution

01

Compute the slope between A and B

First, let's find the slope between points A(-3, 6) and B(3, 3). We need to apply the formula: \[m_{AB} = \frac{y2 - y1}{x2 - x1} = \frac{3-6}{3-(-3)}\]
02

Calculate the slope between A and B

Next, substitute the coordinates of points A and B into the slope formula and calculate the result: \[m_{AB} = \frac{-3}{6} = -\frac{1}{2}\]
03

Compute the slope between B and C

Now, let's find the slope between points B(3, 3) and C(6, 0). We need to apply the same formula as before: \[m_{BC} = \frac{y2 - y1}{x2 - x1} = \frac{0 - 3}{6 - 3}\]
04

Calculate the slope between B and C

Substitute the coordinates of points B and C into the slope formula and calculate the result: \[m_{BC} = \frac{-3}{3} = -1\]
05

Compare the slopes

Now we compare the slopes m_{AB} and m_{BC}: \[m_{AB} = -\frac{1}{2} \neq -1 = m_{BC}\] Since the slopes are not equal, the points A(-3, 6), B(3, 3), and C(6, 0) do not lie on a straight line.

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

Plot the graph of the function \(f\) in (a) the standard viewing window and (b) the indicated window. $$ f(x)=x^{3}-20 x^{2}+8 x-10 ; \quad[-20,20] \times[-1200,100] $$

Find the inverse of \(f .\) Then sketch the graphs of \(f\) and \(f^{-1}\) on the same set of axes. $$ f(x)=\sqrt{9-x^{2}}, \quad x \geq 0 $$

Write the expression in algebraic form. $$ \sin \left(\cos ^{-1} x\right) $$

Prove that a function has an inverse if and only if it is oneto-one.

Find \(f^{-1}(a)\) for the function \(f\) and the real number \(a\). $$ f(x)=\frac{3}{\pi} x+\sin x ; \quad-\frac{\pi}{2}
See all solutions

Recommended explanations on Math Textbooks

Logic and Functions

Read Explanation

Mechanics Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Statistics

Read Explanation

Pure Maths

Read Explanation

Geometry

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.