Explanation Given Information: The points are; ( − 2 , 1 ) and ( 4 , 2 ) . Formula used: Distance formula: For two points ( x 1 , y 1 ) and ( x 2 , y 2 ) , the distance between the points is evaluated from the expression, d = ( x 2 − x 1 ) 2 + ( y 2 − y 1 ) 2 Calculation: Consider the points, ( − 2 , 1 ) and ( 4 , 2 ) Use the distance formula, d = ( x 2 − x 1 ) 2 + ( y 2 − y 1 ) 2 Substitute − 2 for x 1 , 1 for y 1 , 4 for x 2 , and 2 for y 2

13th Edition

ISBN: 9780134707365

Author: Marvin L. Bittinger, Judith A. Beecher, Barbara L. Johnson

Publisher: PEARSON

See similar textbooks

Concept explainers

Family of Curves

A family of curves is a group of curves that are each described by a parametrization in which one or more variables are parameters. In general, the parameters have more complexity on the assembly of the curve than an ordinary linear transformation. These…

XZ Plane

In order to understand XZ plane, it's helpful to understand two-dimensional and three-dimensional spaces. To plot a point on a plane, two numbers are needed, and these two numbers in the plane can be represented as an ordered pair (a,b) where a and b are…

Euclidean Geometry

Geometry is the branch of mathematics that deals with flat surfaces like lines, angles, points, two-dimensional figures, etc. In Euclidean geometry, one studies the geometrical shapes that rely on different theorems and axioms. This (pure mathematics) ge…

Lines and Angles

In a two-dimensional plane, a line is simply a figure that joins two points. Usually, lines are used for presenting objects that are straight in shape and have minimal depth or width.

Videos

Question

Chapter 9.1, Problem 5DE

To determine

To calculate: The distance between the points (−2,1) and (4,2).

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 9.1, Problem 4DE

Chapter 9.1, Problem 6DE

Students have asked these similar questions

ے ملزمة احمد Q (a) Let f be a linear map from a space X into a space Y and (X1,X2,...,xn) basis for X, show that fis one-to- one iff (f(x1),f(x2),...,f(x) } linearly independent. (b) Let X= {ao+ax₁+a2x2+...+anxn, a;ER} be a vector space over R, write with prove a hyperspace and a hyperplane of X. مبر خد احمد Q₂ (a) Let M be a subspace of a vector space X, and A= {fex/ f(x)=0, x E M ), show that whether A is convex set or not, affine set or not. Write with prove an application of Hahn-Banach theorem. Show that every singleton set in a normed space X is closed and any finite set in X is closed (14M)

Let M be a proper subspace of a finite dimension vector space X over a field F show that whether: (1) If S is a base for M then S base for X or not, (2) If T base for X then base for M or not. (b) Let X-P₂(x) be a vector space over polynomials a field of real numbers R, write with L prove convex subset of X and hyperspace of X. Q₂/ (a) Let X-R³ be a vector space over a over a field of real numbers R and A=((a,b,o), a,bE R), A is a subspace of X, let g be a function from A into R such that gla,b,o)-a, gEA, find fe X such that g(t)=f(t), tEA. (b) Let M be a non-empty subset of a space X, show that M is a hyperplane of X iff there Xiff there exists fE X/10) and tE F such that M=(xE X/ f(x)=t). (c) Show that the relation equivalent is an equivalence relation on set of norms on a space X.

Q/(a)Let X be a finite dimension vector space over a field F and S₁,S2CX such that S₁SS2. Show that whether (1) if S, is a base for X then base for X or not (2) if S2 is a base for X then S, is a base for X or not (b) Show that every subspace of vector space is convex and affine set but the conevrse need not to be true. allet M be a non-empty subset of a vector space X over a field F and x,EX. Show that M is a hyperspace iff xo+ M is a hyperplane and xo€ xo+M. bState Hahn-Banach theorem and write with prove an application about it. Show that every singleten subset and finite subset of a normed space is closed. Oxfallet f he a function from a normad roace YI Show tha ir continuour aty.GYiff

Chapter 9 Solutions

Intermediate Algebra (13th Edition)

Ch. 9.1 - Prob. 1SR Ch. 9.1 - Prob. 2SR Ch. 9.1 - Prob. 1DE Ch. 9.1 - Prob. 2DE Ch. 9.1 - Prob. 1CCE Ch. 9.1 - Prob. 2CCE Ch. 9.1 - Prob. 3CCE Ch. 9.1 - Prob. 3DE Ch. 9.1 - Prob. 4DE Ch. 9.1 - Prob. 5DE

Knowledge Booster

$Algebra$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.

The distance between the points ( − 2 , 1 ) and ( 4 , 2 ) .

Solution Summary: The author calculates the distance between the points (-2,1) and

Concept explainers

Videos

To calculate: The distance between the points (−2,1) and (4,2).

Want to see the full answer?

Chapter 9 Solutions