McDougal Littell Jurgensen Geometry: Student Edition Geometry

5th Edition

ISBN: 9780395977279

Author: Ray C. Jurgensen, Richard G. Brown, John W. Jurgensen

Publisher: Houghton Mifflin Company College Division

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Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on …

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Question

Chapter 2.3, Problem 19WE

To determine

To fill : In the blanks in the table using the given information.

Expert Solution & Answer

Answer to Problem 19WE

Statement		Reasons
1.	A , M and B have coordinates a, x and b respectively; b>a	1.	Given information
2.	AM=x−aMB=b−x	2.	Ruler Angle Postulate
3.	M is the mid-point of AB→	3.	Given information.
4.	BM→≅AM→ or AM=BM	4.	Definition of mid-point theorem
5.	x−a=b−x	5.	Substitution Property(Step 2 and Step 4)
6.	2x=a+b	6.	Addition Property from algebra
7.	x=a+b2	7.	Division property from algebra

Explanation of Solution

Given information : Given that points A and B have coordinates a and b ; b>a and the midpoint M of AB→ has coordinate x and it is to be proven that x=a+b2 .

The conditional “If A and B have coordinates a and b, with b>a and the midpoint M of AB→ has coordinate x then x=a+b2 ” is to be proved by a two column proof.

The reasons used in the proof are to be filled in the table that follows.

Statement 1 states that A , M and B have coordinates a , x and b which are given so the reason used to prove it is “Given information”.

Consider the figure which is given, pointsa , x and b are aligned in such a way that the distance between either ofA , M and B equals the absolute value of the difference of the coordinates, So the reason for AM=x−a or MB=b−x is the “ruler angle postulate ” which is accepted without proof.

Statement 3 states that M is the mid-point of AB→ which is given so the reason used to prove it is “Given information”.

The midpoint theorem states that ifM is the mid-point of AB→ so AM=12AB or MB=12AB which gives AM=MB so the reason for statement 4 is “Definition of Midpoint theorem.”

Consider step 2 and step 4, substitute AM=x−a and MB=b−x in AM = BMwhich gives, x−a=b−x , so the reason for statement 5 is “Substitution Property(Step 2 and Step 4)”.

Consider 2x=? , from step 5, x−a=b−x⇒2x=a+b .The reason for statement 6 becomes “Addition property from algebra.”

Division property from algebra states that if a=b then ac=bc . In statement 6, 2x=a+b ,divide both sides by 2 to get x=a+b2 .

Statement		Reasons
1.	A , M and B have coordinates a, x and b respectively; b>a	1.	Given information
2.	AM=x−a; MB=b−x	2.	Ruler Angle Postulate
3.	M is the mid-point of AB→	3.	Given information.
4.	BM→≅AM→ or AM=BM	4.	Definition of mid-point theorem
5.	x−a=b−x	5.	Substitution Property(Step 2 and Step 4)
6.	2x=a+b	6.	Addition Property from algebra
7.	x=a+b2	7.	Division property from algebra

Chapter 2.3, Problem 18WE

Chapter 2.3, Problem 20WE

Chapter 2 Solutions

McDougal Littell Jurgensen Geometry: Student Edition Geometry

Ch. 2.1 - Prob. 1CE Ch. 2.1 - Prob. 2CE Ch. 2.1 - Prob. 3CE Ch. 2.1 - Prob. 4CE Ch. 2.1 - Prob. 5CE Ch. 2.1 - Prob. 6CE Ch. 2.1 - Prob. 7CE Ch. 2.1 - Prob. 8CE Ch. 2.1 - Prob. 9CE Ch. 2.1 - Prob. 10CE

Ch. 2.1 - Prob. 11CE Ch. 2.1 - Prob. 12CE Ch. 2.1 - Prob. 13CE Ch. 2.1 - Prob. 14CE Ch. 2.1 - Prob. 15CE Ch. 2.1 - Prob. 16CE Ch. 2.1 - Prob. 1WE Ch. 2.1 - Prob. 2WE Ch. 2.1 - Prob. 3WE Ch. 2.1 - Prob. 4WE Ch. 2.1 - Prob. 5WE Ch. 2.1 - Prob. 6WE Ch. 2.1 - Prob. 7WE Ch. 2.1 - Prob. 8WE Ch. 2.1 - Prob. 9WE Ch. 2.1 - Prob. 10WE Ch. 2.1 - Prob. 11WE Ch. 2.1 - Prob. 12WE Ch. 2.1 - Prob. 13WE Ch. 2.1 - Prob. 14WE Ch. 2.1 - Prob. 15WE Ch. 2.1 - Prob. 16WE Ch. 2.1 - Prob. 17WE Ch. 2.1 - Prob. 18WE Ch. 2.1 - Prob. 19WE Ch. 2.1 - Prob. 20WE Ch. 2.1 - Prob. 21WE Ch. 2.1 - Prob. 22WE Ch. 2.1 - Prob. 23WE Ch. 2.1 - Prob. 24WE Ch. 2.1 - Prob. 25WE Ch. 2.1 - Prob. 26WE Ch. 2.1 - Prob. 27WE Ch. 2.1 - Prob. 28WE Ch. 2.1 - Prob. 29WE Ch. 2.1 - Prob. 30WE Ch. 2.1 - Prob. 31WE Ch. 2.1 - Prob. 1MRE Ch. 2.1 - Prob. 2MRE Ch. 2.1 - Prob. 3MRE Ch. 2.1 - Prob. 4MRE Ch. 2.2 - Prob. 1CE Ch. 2.2 - Prob. 2CE Ch. 2.2 - Prob. 3CE Ch. 2.2 - Prob. 4CE Ch. 2.2 - Prob. 5CE Ch. 2.2 - Prob. 6CE Ch. 2.2 - Prob. 7CE Ch. 2.2 - Prob. 8CE Ch. 2.2 - Prob. 9CE Ch. 2.2 - Prob. 10CE Ch. 2.2 - Prob. 11CE Ch. 2.2 - Prob. 12CE Ch. 2.2 - Prob. 1WE Ch. 2.2 - Prob. 2WE Ch. 2.2 - Prob. 3WE Ch. 2.2 - Prob. 4WE Ch. 2.2 - Prob. 5WE Ch. 2.2 - Prob. 6WE Ch. 2.2 - Prob. 7WE Ch. 2.2 - Prob. 8WE Ch. 2.2 - Prob. 9WE Ch. 2.2 - Prob. 10WE Ch. 2.2 - Prob. 11WE Ch. 2.2 - Prob. 12WE Ch. 2.2 - Prob. 13WE Ch. 2.2 - Prob. 14WE Ch. 2.2 - Prob. 15WE Ch. 2.3 - Prob. 1CE Ch. 2.3 - Prob. 2CE Ch. 2.3 - Prob. 3CE Ch. 2.3 - Prob. 4CE Ch. 2.3 - Prob. 5CE Ch. 2.3 - Prob. 6CE Ch. 2.3 - Prob. 7CE Ch. 2.3 - Prob. 8CE Ch. 2.3 - Prob. 9CE Ch. 2.3 - Prob. 10CE Ch. 2.3 - Prob. 1WE Ch. 2.3 - Prob. 2WE Ch. 2.3 - Prob. 3WE Ch. 2.3 - Prob. 4WE Ch. 2.3 - Prob. 5WE Ch. 2.3 - Prob. 6WE Ch. 2.3 - Prob. 7WE Ch. 2.3 - Prob. 8WE Ch. 2.3 - Prob. 9WE Ch. 2.3 - Prob. 10WE Ch. 2.3 - Prob. 11WE Ch. 2.3 - Prob. 12WE Ch. 2.3 - Prob. 13WE Ch. 2.3 - Prob. 14WE Ch. 2.3 - Prob. 15WE Ch. 2.3 - Prob. 16WE Ch. 2.3 - Prob. 17WE Ch. 2.3 - Prob. 18WE Ch. 2.3 - Prob. 19WE Ch. 2.3 - Prob. 20WE Ch. 2.3 - Prob. 21WE Ch. 2.3 - Prob. 22WE Ch. 2.3 - Prob. 1E Ch. 2.3 - Prob. 2E Ch. 2.3 - Prob. 3E Ch. 2.3 - Prob. 1ST1 Ch. 2.3 - Prob. 2ST1 Ch. 2.3 - Prob. 3ST1 Ch. 2.3 - Prob. 4ST1 Ch. 2.3 - Prob. 5ST1 Ch. 2.3 - Prob. 6ST1 Ch. 2.3 - Prob. 7ST1 Ch. 2.3 - Prob. 8ST1 Ch. 2.4 - Prob. 1CE Ch. 2.4 - Prob. 2CE Ch. 2.4 - Prob. 3CE Ch. 2.4 - Prob. 4CE Ch. 2.4 - Prob. 5CE Ch. 2.4 - Prob. 6CE Ch. 2.4 - Prob. 7CE Ch. 2.4 - Prob. 8CE Ch. 2.4 - Prob. 9CE Ch. 2.4 - Prob. 10CE Ch. 2.4 - Prob. 11CE Ch. 2.4 - Prob. 12CE Ch. 2.4 - Prob. 13CE Ch. 2.4 - Prob. 14CE Ch. 2.4 - Prob. 15CE Ch. 2.4 - Prob. 16CE Ch. 2.4 - Prob. 17CE Ch. 2.4 - Prob. 18CE Ch. 2.4 - Prob. 19CE Ch. 2.4 - Prob. 20CE Ch. 2.4 - Prob. 21CE Ch. 2.4 - Prob. 1WE Ch. 2.4 - Prob. 2WE Ch. 2.4 - Prob. 3WE Ch. 2.4 - Prob. 4WE Ch. 2.4 - Prob. 5WE Ch. 2.4 - Prob. 6WE Ch. 2.4 - Prob. 7WE Ch. 2.4 - Prob. 8WE Ch. 2.4 - Prob. 9WE Ch. 2.4 - Prob. 10WE Ch. 2.4 - Prob. 11WE Ch. 2.4 - Prob. 12WE Ch. 2.4 - Prob. 13WE Ch. 2.4 - Prob. 14WE Ch. 2.4 - Prob. 15WE Ch. 2.4 - Prob. 16WE Ch. 2.4 - Prob. 17WE Ch. 2.4 - Prob. 18WE Ch. 2.4 - Prob. 19WE Ch. 2.4 - Prob. 20WE Ch. 2.4 - Prob. 21WE Ch. 2.4 - Prob. 22WE Ch. 2.4 - Prob. 23WE Ch. 2.4 - Prob. 24WE Ch. 2.4 - Prob. 25WE Ch. 2.4 - Prob. 26WE Ch. 2.4 - Prob. 27WE Ch. 2.4 - Prob. 28WE Ch. 2.4 - Prob. 29WE Ch. 2.4 - Prob. 30WE Ch. 2.4 - Prob. 31WE Ch. 2.4 - Prob. 32WE Ch. 2.4 - Prob. 33WE Ch. 2.4 - Prob. 34WE Ch. 2.4 - Prob. 35WE Ch. 2.4 - Prob. 1E Ch. 2.4 - Prob. 2E Ch. 2.4 - Prob. 3E Ch. 2.4 - Prob. 4E Ch. 2.5 - Prob. 1CE Ch. 2.5 - Prob. 2CE Ch. 2.5 - Prob. 3CE Ch. 2.5 - Prob. 4CE Ch. 2.5 - Prob. 5CE Ch. 2.5 - Prob. 6CE Ch. 2.5 - Prob. 7CE Ch. 2.5 - Prob. 8CE Ch. 2.5 - Prob. 9CE Ch. 2.5 - Prob. 10CE Ch. 2.5 - Prob. 11CE Ch. 2.5 - Prob. 1WE Ch. 2.5 - Prob. 2WE Ch. 2.5 - Prob. 3WE Ch. 2.5 - Prob. 4WE Ch. 2.5 - Prob. 5WE Ch. 2.5 - Prob. 6WE Ch. 2.5 - Prob. 7WE Ch. 2.5 - Prob. 8WE Ch. 2.5 - Prob. 9WE Ch. 2.5 - Prob. 10WE Ch. 2.5 - Prob. 11WE Ch. 2.5 - Prob. 12WE Ch. 2.5 - Prob. 13WE Ch. 2.5 - Prob. 14WE Ch. 2.5 - Prob. 15WE Ch. 2.5 - Prob. 16WE Ch. 2.5 - Prob. 17WE Ch. 2.5 - Prob. 18WE Ch. 2.5 - Prob. 19WE Ch. 2.5 - Prob. 20WE Ch. 2.5 - Prob. 21WE Ch. 2.5 - Prob. 22WE Ch. 2.5 - Prob. 23WE Ch. 2.5 - Prob. 24WE Ch. 2.5 - Prob. 25WE Ch. 2.5 - Prob. 26WE Ch. 2.5 - Prob. 27WE Ch. 2.5 - Prob. 28WE Ch. 2.5 - Prob. 29WE Ch. 2.5 - Prob. 1MRE Ch. 2.5 - Prob. 2MRE Ch. 2.5 - Prob. 3MRE Ch. 2.5 - Prob. 4MRE Ch. 2.5 - Prob. 5MRE Ch. 2.5 - Prob. 6MRE Ch. 2.5 - Prob. 7MRE Ch. 2.6 - Prob. 1CE Ch. 2.6 - Prob. 2CE Ch. 2.6 - Prob. 3CE Ch. 2.6 - Prob. 4CE Ch. 2.6 - Prob. 5CE Ch. 2.6 - Prob. 6CE Ch. 2.6 - Prob. 7CE Ch. 2.6 - Prob. 8CE Ch. 2.6 - Prob. 9CE Ch. 2.6 - Prob. 10CE Ch. 2.6 - Prob. 1WE Ch. 2.6 - Prob. 2WE Ch. 2.6 - Prob. 3WE Ch. 2.6 - Prob. 4WE Ch. 2.6 - Prob. 5WE Ch. 2.6 - Prob. 6WE Ch. 2.6 - Prob. 7WE Ch. 2.6 - Prob. 8WE Ch. 2.6 - Prob. 9WE Ch. 2.6 - Prob. 10WE Ch. 2.6 - Prob. 11WE Ch. 2.6 - Prob. 12WE Ch. 2.6 - Prob. 13WE Ch. 2.6 - Prob. 14WE Ch. 2.6 - Prob. 15WE Ch. 2.6 - Prob. 16WE Ch. 2.6 - Prob. 17WE Ch. 2.6 - Prob. 18WE Ch. 2.6 - Prob. 19WE Ch. 2.6 - Prob. 20WE Ch. 2.6 - Prob. 21WE Ch. 2.6 - Prob. 22WE Ch. 2.6 - Prob. 23WE Ch. 2.6 - Prob. 24WE Ch. 2.6 - Prob. 25WE Ch. 2.6 - Prob. 1ST2 Ch. 2.6 - Prob. 2ST2 Ch. 2.6 - Prob. 3ST2 Ch. 2.6 - Prob. 4ST2 Ch. 2.6 - Prob. 5ST2 Ch. 2.6 - Prob. 6ST2 Ch. 2.6 - Prob. 7ST2 Ch. 2.6 - Prob. 8ST2 Ch. 2.6 - Prob. 9ST2 Ch. 2.6 - Prob. 1E Ch. 2.6 - Prob. 2E Ch. 2.6 - Prob. 3E Ch. 2.6 - Prob. 4E Ch. 2.6 - Prob. 5E Ch. 2 - Prob. 1CR Ch. 2 - Prob. 2CR Ch. 2 - Prob. 3CR Ch. 2 - Prob. 4CR Ch. 2 - Prob. 5CR Ch. 2 - Prob. 6CR Ch. 2 - Prob. 7CR Ch. 2 - Prob. 8CR Ch. 2 - Prob. 9CR Ch. 2 - Prob. 10CR Ch. 2 - Prob. 11CR Ch. 2 - Prob. 12CR Ch. 2 - Prob. 13CR Ch. 2 - Prob. 14CR Ch. 2 - Prob. 15CR Ch. 2 - Prob. 16CR Ch. 2 - Prob. 17CR Ch. 2 - Prob. 18CR Ch. 2 - Prob. 19CR Ch. 2 - Prob. 20CR Ch. 2 - Prob. 1CT Ch. 2 - Prob. 2CT Ch. 2 - Prob. 3CT Ch. 2 - Prob. 4CT Ch. 2 - Prob. 5CT Ch. 2 - Prob. 6CT Ch. 2 - Prob. 7CT Ch. 2 - Prob. 8CT Ch. 2 - Prob. 9CT Ch. 2 - Prob. 10CT Ch. 2 - Prob. 11CT Ch. 2 - Prob. 12CT Ch. 2 - Prob. 1AR Ch. 2 - Prob. 2AR Ch. 2 - Prob. 3AR Ch. 2 - Prob. 4AR Ch. 2 - Prob. 5AR Ch. 2 - Prob. 6AR Ch. 2 - Prob. 7AR Ch. 2 - Prob. 8AR Ch. 2 - Prob. 9AR Ch. 2 - Prob. 10AR Ch. 2 - Prob. 11AR Ch. 2 - Prob. 12AR Ch. 2 - Prob. 13AR Ch. 2 - Prob. 14AR Ch. 2 - Prob. 15AR Ch. 2 - Prob. 16AR Ch. 2 - Prob. 17AR Ch. 2 - Prob. 18AR Ch. 2 - Prob. 1CUR Ch. 2 - Prob. 2CUR Ch. 2 - Prob. 3CUR Ch. 2 - Prob. 4CUR Ch. 2 - Prob. 5CUR Ch. 2 - Prob. 6CUR Ch. 2 - Prob. 7CUR Ch. 2 - Prob. 8CUR Ch. 2 - Prob. 9CUR Ch. 2 - Prob. 10CUR Ch. 2 - Prob. 11CUR Ch. 2 - Prob. 12CUR Ch. 2 - Prob. 13CUR Ch. 2 - Prob. 14CUR Ch. 2 - Prob. 15CUR Ch. 2 - Prob. 16CUR Ch. 2 - Prob. 17CUR Ch. 2 - Prob. 18CUR Ch. 2 - Prob. 19CUR Ch. 2 - Prob. 20CUR Ch. 2 - Prob. 21CUR Ch. 2 - Prob. 22CUR Ch. 2 - Prob. 23CUR Ch. 2 - Prob. 24CUR Ch. 2 - Prob. 25CUR

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