10­09 Writing Parallel and Perpendicular Lines with Answers.notebook

1

October 06, 2015

Feb 21­12:49 PM

10/09/15Writing Equations of Parallel and

Perpendicular Lines

G.GPE.5 Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point).

EQ: What is the relationship between the slopes of parallel lines? perpendicular lines?

Hemp thread

Lee Street

The local recreation department has created a map of its newest baseball field. The bases and home plate of a baseball diamond form a square, meaning opposite sides are parallel and adjacent sides are perpendicular and all sides are congruent. First base is represented by the point (7, ‐3), second base is represented by (4, 6), third base is represented by (‐5, 3), and home plate is represented by (‐2, ‐6).

1. Find the slopes of the following:a. home plate to 1st base b.1st base to 2nd base c. 2nd base to 3rd base d. 3rd base to home

2. Which sides of the baseball diamond are parallel (there are 2 sets)? Explain how you chose these.

3. Which sides of the baseball diamond are perpendicular (there are 4 sets)? Explain how you chose these.

4. Civil engineers are planning a new shopping center downtown. They would like the entrance to the center to run perpendicular to the street represented by the equation

a. Write an equation that would represent the entrance to the shopping center. (find the slope, sketch, and then write an equation.)

b. A second entrance will run parallel to the first entrance. Write an equation that would represent the second entranceto the shopping center. (find the slope, sketch, and then write an equation.)

home to 1st 2nd to 3rd

1st to 2nd 3rd to homeEach set has identical slopes

home to 1st 1st to 2ndhome to 1st 3rd to home

2nd to 3rd 3rd to home1st to 2nd 2nd to 3rd

Each set has oppositereciprocal slopes

y = ‐5x + (any number)

y = ‐5x + (any number other than what you used in a)

Homework Answers

Sep 27 ­ 6:28 PM

Ticket Time!

Hemp thread

Put the following equations in slope‐intercept form. Determine the slope, parallel slope, and perpendicular slope.

Warm­up

1. 3y = 2x ‐ 3 2. 3x ‐ y = 5 3. 9x + 3y = 83 3

y = 2/3 x - 22/3

2/3

-3/2

-3x -3x-y = -3x + 5

y = 3x - 53

3

-1/3

-1 -1

-9x -9x3y = -9x + 83 3

y = -3x + 8/3-3

-3

1/3

Hemp thread

Let’s review how to write the equation of the line that passes through the two points. First, determine the slope. Then substitute the slope and either point into to write the equation of the line.

Let's Review

1. (2, 6) and (‐1, 3) 2. (‐4, 8) and (3, 8) 3. (2, ‐5) and (2, 7)

3 - 6 -1 - 2

-3 -3

= 1=

m = 1; (2,6)

y - 6 = 1(x - 2)y - 6 = x - 2 +6 +6 y = x + 4

8 - 8 3 + 4

= 0 7

= 0

m = 0

horizontal

y = 8

m = undefined

vertical

x = 2

7 - -5 2 - 2

= 12 0

Hemp thread

1. Put the given equation in slope‐intercept form in order to get the slope:

m = 4 m = 4

2. Substitute the || slope and given ordered pair in the point‐slope form to find the new equation.

To find a perpendicular equation, you would do the same process, but m = 4 m=

Now, write the slope‐intercept form of an equation that passes through the point (5, ‐2) and is parallel to the graph of 8x ‐ 2y = 6.

Guided Example

10­09 Writing Parallel and Perpendicular Lines with Answers.notebook

2

October 06, 2015

Hemp thread

You Try!1. Write the slope‐intercept form of the equation that passes

through the point (0, 5) and is parallel to a line with a slope of 4.

2. Write the slope‐intercept form of the equation that passes through the point (12, ‐2) and is perpendicular to a line with a slope of 4.

3. Write the slope‐intercept form of the equation that passes through the point (‐4, 10) and is parallel to the graph of .

4. Write the slope‐intercept form of the equation that passes through the point (‐4, 10) and is perpendicular to the graph of .

5. Write the slope‐intercept form of the equation that passes through the point (3, 1) and is parallel to the graph of 4x + 2y = 10.

6. Write the slope‐intercept form of the equation that passes through the point (‐1, 6) and is perpendicular to the graph of ‐10x + 5y = 20.

m = 4; (0, 5)y - 5 = 4(x - 0)y - 5 = 4x +5 +5y = 4x + 5

m = -1/4; (12, -2)y + 2 = -1/4(x - 12)y + 2 = -1/4x + 3 -2 -2y = -1/4x + 1

m = 1/2; (-4, 10)y - 10 = 1/2(x + 4)y - 10 = 1/2x + 2 +10 +10y = 1/2x + 12

m = -2; (-4, 10)y - 10 = -2(x + 4)y - 10 = -2x - 8 +10 +10y = -2x + 2

m = -2; (3, 1)y - 1 = -2(x - 3)y - 1 = -2x + 6 +1 +1y = -2x + 7

m = -1/2; (-1, 6)y - 6 = -1/2(x + 1)y - 6 = -1/2x - 1/2 +6 +6y = -1/2x + 11/2

-4x -4x

2y = -4x + 10 2 2 y = -2x + 5m = -2

+10x +10x5y = 10x + 20 5 5 y = 2x + 4m = 2

Mar 22­3:50 PM

Complete Homework

Mar 31­12:06 PM