Category Archives: Trigsted Chapter 2

Example: Find the general form of the circle

(x-8)^2+(y+6)^2=10^2

Solution:

(x-8)^2+(y+6)^2=10^2

(x-8)(x-8)+(y+6)(y+6)=100

x^2-8x-8x+64+y^2+6x+6x+36=100

x^2-16x+64+y^2+36x+36=100

x^2-16x+y^2+36x+100=100

x^2-16x+y^2+36x+100-100=100-100

x^2-16x+y^2+36x=0

2.1 Graphing, Distance

Using the Distance Formula

March 25, 2017 admin

The Distance Formula

Suppose A is ( x_1, y_1) and B is ( x_2, y_2)

The distance between points A and B is given by the following formula.

$d=sqrt {(x_2-x_1)^2+ (y_2-y_1)^2}$

Example: Find the y-coordinate of the points that are 5 units away from the point (3,3) that have an x-coordinate of -1.

$5=sqrt {(-1-3)^2+ (y-3)^2}$

$5=sqrt {(-4)^2+ (y-3)^2}$

$5=sqrt {16+ (y-3)^2}$

$5^2=(sqrt {16+ (y-3)^2})^2$

25=16+ (y-3)^2

25-16=16-16+ (y-3)^2

9= (y-3)^2

$sqrt{9}= sqrt{(y-3)^2}$

pm 3= y-3

3 pm 3= y

3 + 3= y or 3 - 3= y

6= y or 0= y

2.1 Graphing, 3.6 Mathematical Models: Building Functions, Distance

Finding the Distance

March 25, 2017 admin

The Distance Formula

Suppose A is ( x_1, y_1) and B is ( x_2, y_2)

The distance between points A and B is given by the following formula.

$d=sqrt {(x_2-x_1)^2+ (y_2-y_1)^2}$

Example: Find the distance between points A and B.

Point A is ( 4, -2) and point B is ( -8, 3)

$d=sqrt {(-8-4)^2+ (3-(-2))^2}$

$d=sqrt {(-12)^2+ (3+2)^2}$

$d=sqrt {144+ (5)^2}$

d=sqrt {144+ 25}

d=sqrt {169}

d=13

2.1 Graphing, Midpoint

Finding the Midpoint

March 25, 2017 admin

The Midpoint Formula

Suppose A is ( x_1, y_1) and B is ( x_2, y_2)

The midpoint of the line segment joining points A and B is given by the following formula.

$( {x_1+x_2}/2, {y_1+y_2}/2)$

Example: Find the midpoint of a line segment joining points A and B.

Point A is ( 4, -2) and point B is ( -8, 3)

The x coordinate of the midpoint can be found by averaging the x-values of point A and B. The y-coordinate of the midpoint can be found by averaging the y-values of point A and B.

( {4+(-8)}/2, {-2+3}/2)

( {-4}/2, {1}/2)

( -2, {1}/2)

2.2 Lines, 2.3 Lines, Linear Equations

Forms of Linear Equations

March 19, 2017 admin

Slope Intercept Form

y=mx+b

m is the slope of the line and (0,b) is the y-intercept

Point Slope Form

y-y_1=m(x-x_1)

m is the slope of the line and (x_1,y_1) is a point on the line.

Standard Form of a Line

Ax+By=C

2.2 Lines, 2.3 Lines, 4.1 Linear Functions and Their Properties, Graphing with Slope Intercept Form

Graphing Linear Equations with Slope Intercept Form

March 19, 2017 admin

Example: Graph the linear equation using the slope and the y-intercept. (the slope is positive and fractional)

Example: Graph the linear equation using the slope and the y-intercept. (positive and negative fractional slopes)

Example: Graph the linear equation using the slope and the y-intercept. (equation written in standard form)

2.2 Lines, 2.3 Lines, Graphing By Plotting Points

Graphing Horizontal and Vertical Lines

Video March 19, 2017 admin

2.2 Lines, 2.4 Parallel and Perpendicular Lines, Slope

Perpendicular Lines and Parallel Lines

March 19, 2017 admin

Example: What are parallel and perpendicular lines?

Example: How are the slopes of parallel and perpendicular lines related? (only watch until 1 min 20 seconds)

Example: Are the lines parallel, perpendicular or neither?

Example: Are the lines perpendicular to each other?

math15fun.com

Category Archives: Trigsted Chapter 2

Find the Standard Form of a Circle given the Endpoints of the Diameter

Finding the Equation of a Line: Given a parallel line in standard form and a point on the line

Circle: Find General Form from Standard Form

Using the Distance Formula

Finding the Distance

Finding the Midpoint

Forms of Linear Equations

Graphing Linear Equations with Slope Intercept Form

Graphing Horizontal and Vertical Lines

Perpendicular Lines and Parallel Lines

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