/*! 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 7 Find the distance from the point... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 5: Problem 7

Find the distance from the point (1,2) to the line \(4 x-3 y=0\)

Short Answer

Expert verified
The distance from the point (1,2) to the line \(4x - 3y = 0\) is \(\frac{2}{5}\) units.

Step by step solution

01

We first identify the values in our equation and point. A = 4, B = -3, C = 0, x = 1, y = 2 #Step 2: Compute the numerator of the distance formula#

Now, we compute the numerator of the distance formula by plugging in the values of A, B, C, x, and y. Numerator = |4(1) - 3(2) + 0| = |4 - 6 + 0| = |-2| #Step 3: Compute the denominator of the distance formula#
02

Now, we compute the denominator of the distance formula by finding the square root of the sum of the squares of A and B. Denominator = \(\sqrt{4^2 + (-3)^2} = \sqrt{16 + 9} = \sqrt{25}\) #Step 4: Compute the distance between the point and line#

Lastly, we find the distance formula by dividing the Numerator by the Denominator. Distance = \(\frac{|-2|}{\sqrt{25}} = \frac{2}{5}\) Hence, the distance from the point (1,2) to the line \(4x - 3y = 0\) is \(\frac{2}{5}\) units.

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

Use the Gram-Schmidt process to find an orthonormal basis for the subspace of \(\mathbb{R}^{4}\) spanned by \(\mathbf{x}_{1}=(4,2,2,1)^{T}, \mathbf{x}_{2}=(2,0,0,2)^{T}, \mathbf{x}_{3}=\) \((1,1,-1,1)^{T}\)

In \(\mathbb{R}^{n}\) with inner product $$\langle\mathbf{x}, \mathbf{y}\rangle=\mathbf{x}^{T} \mathbf{y}$$ derive a formula for the distance between two vectors \(\mathbf{x}=\left(x_{1}, \ldots, x_{n}\right)^{T}\) and \(\mathbf{y}=\left(y_{1}, \ldots, y_{n}\right)^{T}\)

How many \(n \times n\) permutation matrices are there?

Show that $$\|\mathbf{x}\|_{1}=\sum_{i=1}^{n}\left|x_{i}\right|$$ defines a norm on \(\mathbb{R}^{n}\)

Let \(x_{1}, x_{2}, \ldots, x_{n}\) be distinct points in the interval [-1,1] and let $$A_{i}=\int_{-1}^{1} L_{i}(x) d x, \quad i=1, \ldots, n$$ where the \(L_{i}\) 's are the Lagrange functions for the points \(x_{1}, x_{2}, \ldots, x_{n}\) (a) Explain why the quadrature formula $$\int_{-1}^{1} f(x) d x=A_{1} f\left(x_{1}\right)+\cdots+A_{n} f\left(x_{n}\right)$$ will yield the exact value of the integral whenever \(f(x)\) is a polynomial of degree less than \(n\) (b) Apply the quadrature formula to a polynomial of degree 0 and show that $$A_{1}+A_{2}+\cdots+A_{n}=2$$
See all solutions

Recommended explanations on Math Textbooks

Decision Maths

Read Explanation

Logic and Functions

Read Explanation

Calculus

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Discrete Mathematics

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.