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High School Math Algebra Holt Mcdougal Larson Algebra 2: Student Edition 2012

an equation of the line containing the median that joins the first vertex to the side opposite to it. y = 4 3 x − 20 3 Given information: The ordered pairs given below represent the vertices of a triangle : 8 , 4 , 0 , 0 , 10 , 0 Formula Used: The Midpoint Formula The midpoint formula shown below, gives the midpoint of the line segment joining the points A x 1 , y 1 and B x 2 , y 2 . M x 1 + x 2 2 , y 1 + y 2 2 Slope of the line segment The slope of the line segment joining the points A x 1 , y 1 and B x 2 , y 2 is: m = y 2 − y 1 x 2 − x 1 Equation of the line The equation of a line passing through x 0 , y 0 and having the slope m is: y − y 0 = m x − x 0 Explanation: A median of a triangle is a line segment joining a vertex and the midpoint of the opposite side. So, first step is to find the midpoint between the two opposite vertices 0 , 0 and 10 , 0 . By the midpoint formula, M = x 1 + x 2 2 , y 1 + y 2 2 = 0 + 10 2 , 0 + 0 2 = 10 2 , 0 = 5 , 0 Next step is to find the slope that goes through the above midpoint and the first vertex 8 , 4 . m = y 2 − y 1 x 2 − x 1 = 4 − 0 8 − 5 = 4 3 Then, the equation of the line that passes through the midpoint 5 , 0 and has the slope 4 3 is: y − y 0 = m x − x 0 y − 0 = 4 3 x − 5 y = 4 3 x − 20 3

an equation of the line containing the median that joins the first vertex to the side opposite to it. y = 4 3 x − 20 3 Given information: The ordered pairs given below represent the vertices of a triangle : 8 , 4 , 0 , 0 , 10 , 0 Formula Used: The Midpoint Formula The midpoint formula shown below, gives the midpoint of the line segment joining the points A x 1 , y 1 and B x 2 , y 2 . M x 1 + x 2 2 , y 1 + y 2 2 Slope of the line segment The slope of the line segment joining the points A x 1 , y 1 and B x 2 , y 2 is: m = y 2 − y 1 x 2 − x 1 Equation of the line The equation of a line passing through x 0 , y 0 and having the slope m is: y − y 0 = m x − x 0 Explanation: A median of a triangle is a line segment joining a vertex and the midpoint of the opposite side. So, first step is to find the midpoint between the two opposite vertices 0 , 0 and 10 , 0 . By the midpoint formula, M = x 1 + x 2 2 , y 1 + y 2 2 = 0 + 10 2 , 0 + 0 2 = 10 2 , 0 = 5 , 0 Next step is to find the slope that goes through the above midpoint and the first vertex 8 , 4 . m = y 2 − y 1 x 2 − x 1 = 4 − 0 8 − 5 = 4 3 Then, the equation of the line that passes through the midpoint 5 , 0 and has the slope 4 3 is: y − y 0 = m x − x 0 y − 0 = 4 3 x − 5 y = 4 3 x − 20 3

Holt Mcdougal Larson Algebra 2: Student Edition 2012

Holt Mcdougal Larson Algebra 2: Student Edition 2012

1st Edition

ISBN: 9780547647159

Author: HOLT MCDOUGAL

Publisher: HOLT MCDOUGAL

See similar textbooks

Expert Solution & Answer

Polygon with three sides, three angles, and three vertices. Based on the properties of each side, the types of triangles are scalene (triangle with three three different lengths and three different angles), isosceles (angle with two equal sides and two equal angles), and equilateral (three equal sides and three angles of 60°). The types of angles are acute (less than 90°); obtuse (greater than 90°); and right (90°).

Chapter 8.1, Problem 38E

Solution

To write: an equation of the line containing the median that joins the first vertex to the side opposite to it.

$y=43x−203$

Given information:

The ordered pairs given below represent the vertices of a triangle:

$8,4,0,0,10,0$

Formula Used:

The Midpoint Formula

The midpoint formula shown below, gives the midpoint of the line segment joining the points $Ax1,y1$ and $Bx2,y2$ .

$Mx1+x22,y1+y22$

Slope of the line segment

The slope of the line segment joining the points $Ax1,y1$ and $Bx2,y2$ is:

$m=y2−y1x2−x1$

Equation of the line

The equation of a line passing through $x0,y0$ and having the slope m is:

$y−y0=mx−x0$

Explanation:

A median of a triangle is a line segment joining a vertex and the midpoint of the opposite side.

So, first step is to find the midpoint between the two opposite vertices $0,0$ and $10,0$ .

By the midpoint formula,

$M=x1+x22,y1+y22=0+102,0+02=102,0=5,0$

Next step is to find the slope that goes through the above midpoint and the first vertex $8,4$ .

$m=y2−y1x2−x1=4−08−5=43$

Then, the equation of the line that passes through the midpoint $5,0$ and has the slope $43$ is:

$y−y0=mx−x0y−0=43x−5y=43x−203$

Chapter 8.1, Problem 37E

Chapter 8.1, Problem 39E

Chapter 8 Solutions

Holt Mcdougal Larson Algebra 2: Student Edition 2012

Ch. 8.1 - Prob. 1GP Ch. 8.1 - Prob. 2GP Ch. 8.1 - Prob. 3GP Ch. 8.1 - Prob. 4GP Ch. 8.1 - Prob. 5GP Ch. 8.1 - Prob. 6GP Ch. 8.1 - Prob. 1E Ch. 8.1 - Prob. 2E Ch. 8.1 - Prob. 3E Ch. 8.1 - Prob. 4E

Ch. 8.1 - Prob. 5E Ch. 8.1 - Prob. 6E Ch. 8.1 - Prob. 7E Ch. 8.1 - Prob. 8E Ch. 8.1 - Prob. 9E Ch. 8.1 - Prob. 10E Ch. 8.1 - Prob. 11E Ch. 8.1 - Prob. 12E Ch. 8.1 - Prob. 13E Ch. 8.1 - Prob. 14E Ch. 8.1 - Prob. 15E Ch. 8.1 - Prob. 16E Ch. 8.1 - Prob. 17E Ch. 8.1 - Prob. 18E Ch. 8.1 - Prob. 19E Ch. 8.1 - Prob. 20E Ch. 8.1 - Prob. 21E Ch. 8.1 - Prob. 22E Ch. 8.1 - Prob. 23E Ch. 8.1 - Prob. 24E Ch. 8.1 - Prob. 25E Ch. 8.1 - Prob. 26E Ch. 8.1 - Prob. 27E Ch. 8.1 - Prob. 28E Ch. 8.1 - Prob. 29E Ch. 8.1 - Prob. 30E Ch. 8.1 - Prob. 31E Ch. 8.1 - Prob. 32E Ch. 8.1 - Prob. 33E Ch. 8.1 - Prob. 34E Ch. 8.1 - Prob. 35E Ch. 8.1 - Prob. 36E Ch. 8.1 - Prob. 37E Ch. 8.1 - Prob. 38E Ch. 8.1 - Prob. 39E Ch. 8.1 - Prob. 40E Ch. 8.1 - Prob. 41E Ch. 8.1 - Prob. 42E Ch. 8.1 - Prob. 43E Ch. 8.1 - Prob. 44E Ch. 8.1 - Prob. 45E Ch. 8.1 - Prob. 46E Ch. 8.1 - Prob. 47PS Ch. 8.1 - Prob. 48PS Ch. 8.1 - Prob. 49PS Ch. 8.1 - Prob. 50PS Ch. 8.1 - Prob. 51PS Ch. 8.1 - Prob. 52PS Ch. 8.1 - Prob. 53PS Ch. 8.1 - Prob. 54PS Ch. 8.1 - Prob. 55PS Ch. 8.1 - Prob. 56PS Ch. 8.1 - Prob. 57PS Ch. 8.2 - Prob. 1GP Ch. 8.2 - Prob. 2GP Ch. 8.2 - Prob. 3GP Ch. 8.2 - Prob. 4GP Ch. 8.2 - Prob. 5GP Ch. 8.2 - Prob. 6GP Ch. 8.2 - Prob. 7GP Ch. 8.2 - Prob. 8GP Ch. 8.2 - Prob. 9GP Ch. 8.2 - Prob. 1E Ch. 8.2 - Prob. 2E Ch. 8.2 - Prob. 3E Ch. 8.2 - Prob. 4E Ch. 8.2 - Prob. 5E Ch. 8.2 - Prob. 6E Ch. 8.2 - Prob. 7E Ch. 8.2 - Prob. 8E Ch. 8.2 - Prob. 9E Ch. 8.2 - Prob. 10E Ch. 8.2 - Prob. 11E Ch. 8.2 - Prob. 12E Ch. 8.2 - Prob. 13E Ch. 8.2 - Prob. 14E Ch. 8.2 - Prob. 15E Ch. 8.2 - Prob. 16E Ch. 8.2 - Prob. 17E Ch. 8.2 - Prob. 18E Ch. 8.2 - Prob. 19E Ch. 8.2 - Prob. 20E Ch. 8.2 - Prob. 21E Ch. 8.2 - Prob. 22E Ch. 8.2 - Prob. 23E Ch. 8.2 - Prob. 24E Ch. 8.2 - Prob. 25E Ch. 8.2 - Prob. 26E Ch. 8.2 - Prob. 27E Ch. 8.2 - Prob. 28E Ch. 8.2 - Prob. 29E Ch. 8.2 - Prob. 30E Ch. 8.2 - Prob. 31E Ch. 8.2 - Prob. 32E Ch. 8.2 - Prob. 33E Ch. 8.2 - Prob. 34E Ch. 8.2 - Prob. 35E Ch. 8.2 - Prob. 36E Ch. 8.2 - Prob. 37E Ch. 8.2 - Prob. 38E Ch. 8.2 - Prob. 39E Ch. 8.2 - Prob. 40E Ch. 8.2 - Prob. 41E Ch. 8.2 - Prob. 42E Ch. 8.2 - Prob. 43E Ch. 8.2 - Prob. 44E Ch. 8.2 - Prob. 45E Ch. 8.2 - Prob. 46E Ch. 8.2 - Prob. 47E Ch. 8.2 - Prob. 48E Ch. 8.2 - Prob. 49E Ch. 8.2 - Prob. 50E Ch. 8.2 - Prob. 51E Ch. 8.2 - Prob. 52E Ch. 8.2 - Prob. 53E Ch. 8.2 - Prob. 54E Ch. 8.2 - Prob. 55PS Ch. 8.2 - Prob. 56PS Ch. 8.2 - Prob. 57PS Ch. 8.2 - Prob. 58PS Ch. 8.2 - Prob. 59PS Ch. 8.2 - Prob. 60PS Ch. 8.3 - Prob. 1GP Ch. 8.3 - Prob. 2GP Ch. 8.3 - Prob. 3GP Ch. 8.3 - Prob. 4GP Ch. 8.3 - Prob. 5GP Ch. 8.3 - Prob. 6GP Ch. 8.3 - Prob. 1E Ch. 8.3 - Prob. 2E Ch. 8.3 - Prob. 3E Ch. 8.3 - Prob. 4E Ch. 8.3 - Prob. 5E Ch. 8.3 - Prob. 6E Ch. 8.3 - Prob. 7E Ch. 8.3 - Prob. 8E Ch. 8.3 - Prob. 9E Ch. 8.3 - Prob. 10E Ch. 8.3 - Prob. 11E Ch. 8.3 - Prob. 12E Ch. 8.3 - Prob. 13E Ch. 8.3 - Prob. 14E Ch. 8.3 - Prob. 15E Ch. 8.3 - Prob. 16E Ch. 8.3 - Prob. 17E Ch. 8.3 - Prob. 18E Ch. 8.3 - Prob. 19E Ch. 8.3 - Prob. 20E Ch. 8.3 - Prob. 21E Ch. 8.3 - Prob. 22E Ch. 8.3 - Prob. 23E Ch. 8.3 - Prob. 24E Ch. 8.3 - Prob. 25E Ch. 8.3 - Prob. 26E Ch. 8.3 - Prob. 27E Ch. 8.3 - Prob. 28E Ch. 8.3 - Prob. 29E Ch. 8.3 - Prob. 30E Ch. 8.3 - Prob. 31E Ch. 8.3 - Prob. 32E Ch. 8.3 - Prob. 33E Ch. 8.3 - Prob. 34E Ch. 8.3 - Prob. 35E Ch. 8.3 - Prob. 36E Ch. 8.3 - Prob. 37E Ch. 8.3 - Prob. 38E Ch. 8.3 - Prob. 39E Ch. 8.3 - Prob. 40E Ch. 8.3 - Prob. 41E Ch. 8.3 - Prob. 42E Ch. 8.3 - Prob. 43E Ch. 8.3 - Prob. 44E Ch. 8.3 - Prob. 45E Ch. 8.3 - Prob. 46E Ch. 8.3 - Prob. 47E Ch. 8.3 - Prob. 48E Ch. 8.3 - Prob. 49E Ch. 8.3 - Prob. 50E Ch. 8.3 - Prob. 51E Ch. 8.3 - Prob. 52E Ch. 8.3 - Prob. 53E Ch. 8.3 - Prob. 54E Ch. 8.3 - Prob. 55E Ch. 8.3 - Prob. 56E Ch. 8.3 - Prob. 57E Ch. 8.3 - Prob. 58E Ch. 8.3 - Prob. 59E Ch. 8.3 - Prob. 60E Ch. 8.3 - Prob. 61E Ch. 8.3 - Prob. 62PS Ch. 8.3 - Prob. 63PS Ch. 8.3 - Prob. 64PS Ch. 8.3 - Prob. 65PS Ch. 8.3 - Prob. 66PS Ch. 8.3 - Prob. 67PS Ch. 8.3 - Prob. 68PS Ch. 8.3 - Prob. 69PS Ch. 8.3 - Prob. 1Q Ch. 8.3 - Prob. 2Q Ch. 8.3 - Prob. 3Q Ch. 8.3 - Prob. 4Q Ch. 8.3 - Prob. 5Q Ch. 8.3 - Prob. 6Q Ch. 8.3 - Prob. 7Q Ch. 8.3 - Prob. 8Q Ch. 8.3 - Prob. 9Q Ch. 8.3 - Prob. 10Q Ch. 8.3 - Prob. 11Q Ch. 8.3 - Prob. 12Q Ch. 8.3 - Prob. 13Q Ch. 8.3 - Prob. 14Q Ch. 8.3 - Prob. 15Q Ch. 8.3 - Prob. 16Q Ch. 8.3 - Prob. 17Q Ch. 8.3 - Prob. 18Q Ch. 8.3 - Prob. 19Q Ch. 8.3 - Prob. 1P Ch. 8.3 - Prob. 2P Ch. 8.3 - Prob. 3P Ch. 8.3 - Prob. 4P Ch. 8.3 - Prob. 5P Ch. 8.3 - Prob. 6P Ch. 8.4 - Prob. 1GP Ch. 8.4 - Prob. 2GP Ch. 8.4 - Prob. 3GP Ch. 8.4 - Prob. 4GP Ch. 8.4 - Prob. 5GP Ch. 8.4 - Prob. 6GP Ch. 8.4 - Prob. 7GP Ch. 8.4 - Prob. 8GP Ch. 8.4 - Prob. 1E Ch. 8.4 - Prob. 2E Ch. 8.4 - Prob. 3E Ch. 8.4 - Prob. 4E Ch. 8.4 - Prob. 5E Ch. 8.4 - Prob. 6E Ch. 8.4 - Prob. 7E Ch. 8.4 - Prob. 8E Ch. 8.4 - Prob. 9E Ch. 8.4 - Prob. 10E Ch. 8.4 - Prob. 11E Ch. 8.4 - Prob. 12E Ch. 8.4 - Prob. 13E Ch. 8.4 - Prob. 14E Ch. 8.4 - Prob. 15E Ch. 8.4 - Prob. 16E Ch. 8.4 - Prob. 17E Ch. 8.4 - Prob. 18E Ch. 8.4 - Prob. 19E Ch. 8.4 - Prob. 20E Ch. 8.4 - Prob. 21E Ch. 8.4 - Prob. 22E Ch. 8.4 - Prob. 23E Ch. 8.4 - Prob. 24E Ch. 8.4 - Prob. 25E Ch. 8.4 - Prob. 26E Ch. 8.4 - Prob. 27E Ch. 8.4 - Prob. 28E Ch. 8.4 - Prob. 29E Ch. 8.4 - Prob. 30E Ch. 8.4 - Prob. 31E Ch. 8.4 - Prob. 32E Ch. 8.4 - Prob. 33E Ch. 8.4 - Prob. 34E Ch. 8.4 - Prob. 35E Ch. 8.4 - Prob. 36E Ch. 8.4 - Prob. 37E Ch. 8.4 - Prob. 38E Ch. 8.4 - Prob. 39E Ch. 8.4 - Prob. 40E Ch. 8.4 - Prob. 41E Ch. 8.4 - Prob. 42E Ch. 8.4 - Prob. 43E Ch. 8.4 - Prob. 44E Ch. 8.4 - Prob. 45E Ch. 8.4 - Prob. 46E Ch. 8.4 - Prob. 47E Ch. 8.4 - Prob. 48PS Ch. 8.4 - Prob. 49PS Ch. 8.4 - Prob. 50PS Ch. 8.4 - Prob. 51PS Ch. 8.4 - Prob. 52PS Ch. 8.4 - Prob. 53PS Ch. 8.4 - Prob. 1P Ch. 8.4 - Prob. 2P Ch. 8.4 - Prob. 3P Ch. 8.4 - Prob. 1MRPS Ch. 8.4 - Prob. 2MRPS Ch. 8.4 - Prob. 3MRPS Ch. 8.4 - Prob. 4MRPS Ch. 8.4 - Prob. 5MRPS Ch. 8.4 - Prob. 6MRPS Ch. 8.4 - Prob. 7MRPS Ch. 8.4 - Prob. 8MRPS Ch. 8.4 - Prob. 9MRPS Ch. 8.5 - Prob. 1GP Ch. 8.5 - Prob. 2GP Ch. 8.5 - Prob. 3GP Ch. 8.5 - Prob. 4GP Ch. 8.5 - Prob. 5GP Ch. 8.5 - Prob. 6GP Ch. 8.5 - Prob. 1E Ch. 8.5 - Prob. 2E Ch. 8.5 - Prob. 3E Ch. 8.5 - Prob. 4E Ch. 8.5 - Prob. 5E Ch. 8.5 - Prob. 6E Ch. 8.5 - Prob. 7E Ch. 8.5 - Prob. 8E Ch. 8.5 - Prob. 9E Ch. 8.5 - Prob. 10E Ch. 8.5 - Prob. 11E Ch. 8.5 - Prob. 12E Ch. 8.5 - Prob. 13E Ch. 8.5 - Prob. 14E Ch. 8.5 - Prob. 15E Ch. 8.5 - Prob. 16E Ch. 8.5 - Prob. 17E Ch. 8.5 - Prob. 18E Ch. 8.5 - Prob. 19E Ch. 8.5 - Prob. 20E Ch. 8.5 - Prob. 21E Ch. 8.5 - Prob. 22E Ch. 8.5 - Prob. 23E Ch. 8.5 - Prob. 24E Ch. 8.5 - Prob. 25E Ch. 8.5 - Prob. 26E Ch. 8.5 - Prob. 27E Ch. 8.5 - Prob. 28E Ch. 8.5 - Prob. 29E Ch. 8.5 - Prob. 30E Ch. 8.5 - Prob. 31E Ch. 8.5 - Prob. 32E Ch. 8.5 - Prob. 33E Ch. 8.5 - Prob. 34E Ch. 8.5 - Prob. 35E Ch. 8.5 - Prob. 36E Ch. 8.5 - Prob. 37E Ch. 8.5 - Prob. 38PS Ch. 8.5 - Prob. 39PS Ch. 8.5 - Prob. 40PS Ch. 8.5 - Prob. 41PS Ch. 8.5 - Prob. 42PS Ch. 8.5 - Prob. 43PS Ch. 8.5 - Prob. 44PS Ch. 8.5 - Prob. 1Q Ch. 8.5 - Prob. 2Q Ch. 8.5 - Prob. 3Q Ch. 8.5 - Prob. 4Q Ch. 8.5 - Prob. 5Q Ch. 8.5 - Prob. 6Q Ch. 8.5 - Prob. 7Q Ch. 8.5 - Prob. 8Q Ch. 8.5 - Prob. 9Q Ch. 8.5 - Prob. 10Q Ch. 8.5 - Prob. 11Q Ch. 8.5 - Prob. 12Q Ch. 8.5 - Prob. 13Q Ch. 8.6 - Prob. 1GP Ch. 8.6 - Prob. 2GP Ch. 8.6 - Prob. 3GP Ch. 8.6 - Prob. 4GP Ch. 8.6 - Prob. 5GP Ch. 8.6 - Prob. 6GP Ch. 8.6 - Prob. 7GP Ch. 8.6 - Prob. 8GP Ch. 8.6 - Prob. 9GP Ch. 8.6 - Prob. 10GP Ch. 8.6 - Prob. 11GP Ch. 8.6 - Prob. 12GP Ch. 8.6 - Prob. 13GP Ch. 8.6 - Prob. 14GP Ch. 8.6 - Prob. 1E Ch. 8.6 - Prob. 2E Ch. 8.6 - Prob. 3E Ch. 8.6 - Prob. 4E Ch. 8.6 - Prob. 5E Ch. 8.6 - Prob. 6E Ch. 8.6 - Prob. 7E Ch. 8.6 - Prob. 8E Ch. 8.6 - Prob. 9E Ch. 8.6 - Prob. 10E Ch. 8.6 - Prob. 11E Ch. 8.6 - Prob. 12E Ch. 8.6 - Prob. 13E Ch. 8.6 - Prob. 14E Ch. 8.6 - Prob. 15E Ch. 8.6 - Prob. 16E Ch. 8.6 - Prob. 17E Ch. 8.6 - Prob. 18E Ch. 8.6 - Prob. 19E Ch. 8.6 - Prob. 20E Ch. 8.6 - Prob. 21E Ch. 8.6 - Prob. 22E Ch. 8.6 - Prob. 23E Ch. 8.6 - Prob. 24E Ch. 8.6 - Prob. 25E Ch. 8.6 - Prob. 26E Ch. 8.6 - Prob. 27E Ch. 8.6 - Prob. 28E Ch. 8.6 - Prob. 29E Ch. 8.6 - Prob. 30E Ch. 8.6 - Prob. 31E Ch. 8.6 - Prob. 32E Ch. 8.6 - Prob. 33E Ch. 8.6 - Prob. 34E Ch. 8.6 - Prob. 35E Ch. 8.6 - Prob. 36E Ch. 8.6 - Prob. 37E Ch. 8.6 - Prob. 38E Ch. 8.6 - Prob. 39E Ch. 8.6 - Prob. 40E Ch. 8.6 - Prob. 41E Ch. 8.6 - Prob. 42E Ch. 8.6 - Prob. 43E Ch. 8.6 - Prob. 44E Ch. 8.6 - Prob. 45E Ch. 8.6 - Prob. 46E Ch. 8.6 - Prob. 47E Ch. 8.6 - Prob. 48PS Ch. 8.6 - Prob. 49PS Ch. 8.6 - Prob. 50PS Ch. 8.6 - Prob. 51PS Ch. 8.6 - Prob. 52PS Ch. 8.6 - Prob. 53PS Ch. 8.7 - Prob. 1GP Ch. 8.7 - Prob. 2GP Ch. 8.7 - Prob. 3GP Ch. 8.7 - Prob. 4GP Ch. 8.7 - Prob. 5GP Ch. 8.7 - Prob. 6GP Ch. 8.7 - Prob. 7GP Ch. 8.7 - Prob. 8GP Ch. 8.7 - Prob. 9GP Ch. 8.7 - Prob. 10GP Ch. 8.7 - Prob. 1E Ch. 8.7 - Prob. 2E Ch. 8.7 - Prob. 3E Ch. 8.7 - Prob. 4E Ch. 8.7 - Prob. 5E Ch. 8.7 - Prob. 6E Ch. 8.7 - Prob. 7E Ch. 8.7 - Prob. 8E Ch. 8.7 - Prob. 9E Ch. 8.7 - Prob. 10E Ch. 8.7 - Prob. 11E Ch. 8.7 - Prob. 12E Ch. 8.7 - Prob. 13E Ch. 8.7 - Prob. 14E Ch. 8.7 - Prob. 15E Ch. 8.7 - Prob. 16E Ch. 8.7 - Prob. 17E Ch. 8.7 - Prob. 18E Ch. 8.7 - Prob. 19E Ch. 8.7 - Prob. 20E Ch. 8.7 - 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