7.5 Parallel and Perpendicular Lines
MPM1D1: Principles of Mathematics
http://www.dpcdsb.org/AMBRO
Minds On: Anticipation Guide
Instructions:
 Check "Agree" or "Disagree" beside each statement below before you start the investigation.
 Compare your choice and explanation with a partner.
 Revisit your choices after you complete your investigation.
 Compare and reflect on the choices you made "after" with the choices that you made "before".
Before
Statement
After
Agree
Disagree
Agree
Disagree
1. For two lines to be parallel, they need
to have the same y-intercept.
2. Two perpendicular lines intersect
with an angle of 90 degrees.
3. City streets in a grid pattern are
organized in parallel and
perpendicular patterns.
5. In a co–ordinate plane, every vertical
line is perpendicular to every
horizontal line.
6. Two lines with negative slopes must
be parallel.
Action!| Investigating Lines 1
Using Geometer’s Sketchpad
1. Go to the Graph menu
2. Select Plot New Function…
3. Type the equation in y = mx + b form WITHOUT the y (as shown below and do not
use spaces)
4. Click OK
5. Deselect all objects by clicking any white space
6. Repeat steps 1 – 5 for the other two equations
Equation
Graph the Equations
Use a different colour for each equation in a case
a) y = 3x + 4
b) y = 3x – 2
c) y = 3x
Follow up questions:
a) Describe how the lines are similar.
___________________________
b) Describe how the lines are different.
___________________________
c) What do the equations have in common?
___________________________
d) How do the equations differ?
___________________________
e) What is the slope of each line?
y = 3x + 4
y = 3x – 2
y = 3x
m=
m=
m=
f) Write an equation for two NEW lines that are parallel to the series shown above.
new equation 1:
new equation 2:
Action!| Investigating Lines 2
Using Geometer’s Sketchpad
1. Start an new document in Geometer’s Sketchpad by selecting FileNew Sketch
2. Go to the Graph menu
3. Select Plot New Function…
4. Type the equation in y = mx + b form WITHOUT the y (as shown below and do not
use spaces)
5. Click OK
6. Deselect all objects by clicking any white space
7. Repeat steps 1 – 6 for the other two equations
Equation
Graph the Equations
Use a different colour for each line in a case
Case #1:
2
x - 6
3
3
b) y = - x + 2
2
a)
y=
Follow up questions:
a) Estimate the size of the angle formed by these lines. Verify your prediction by measuring the angle
with a protractor.
b) What is the slope of each line?
y=
m=
2
x - 6
3
y=m=
c) Describe how the slopes are related to each other?
3
x+2
2
Equation
Graph the Equations
Use a different colour for each line in a case
Case #2:
1
x+3
4
c)
y=
d)
y = -4x - 5
Follow up questions:
a) Estimate the size of the angle formed by these lines. Verify your prediction by measuring the angle
with a protractor.
b) What is the slope of each line?
y=
1
x+3
4
m=
y = -4x - 5
m=
c) How are these slopes related to each other?
Write a summary of your findings based on these two cases.
With your partner, determine the equations of the other two wires assuming all the lines
are parallel. Test and see if your equations fit the picture on Geometer’s Sketchpad.
With your partner, determine the equation of the cross window cross-frame if both crossframes are perpendicular. Test and see if your equations fit the picture on Geometer’s
Sketchpad.
For each set of equations below, determine the slope of the line and the product of the two slopes.
Set #1:
2
x–6
3
3
b) y = - x + 2
2
a) y =
m=
product of slopes =
m=
Set #2:
a) y =
1
x+3
4
b) y = -4x - 5
m=
product of slopes =
m=
Set #3:
3
x+1
2
2
b) y = - x - 2
3
a) y =
m=
product of slopes =
m=
Set #4:
4
x+3
7
7
b) y = x - 4
4
a) y = -
m=
product of slopes =
m=
Set #5:
1
x+6
3
1
b) y = x + 6
3
a) y =
m=
product of slopes =
m=
Set #6:
m=
a) y = 8x – 5
b)
y=
1
x+2
3
m=
Write a generalization of your findings based on these sets.
product of slopes =
Teacher Sheets: Cut out have students find parallel partner and
then perpendicular partner
Equation
"
y=
2
x+5
3
y = 2x – 3
y=
2
x-5
3
Y=-
2
2
x+
3
3
Y=-
1
x+5
2
y= 
1
x-8
2
y = 2x + 6
y=
1
x–4
4
Y=y=
2
x–5
3
1
x+8
4
Y=-
1
x+2
4
y=
3
x–3
2
y = -4x – 4
Y=Y=
1
x–5
4
3
3
x+
2
2
Y=-
3
x+2
2
y = -4x + 9
y = 4x + 9
"
Equation
3
x+5
5
3
y= x–5
5
5
y=  x–5
3
y=
y = -4x – 4
Y=-
5
x+3
3
y = 3x – 5
3
3
x+
5
5
1
Y=- x+5
3
3
y= x–8
5
Y=-
y = 3x + 6
1
x–4
4
3
y=- x–5
5
1
y= x+8
4
1
Y=- x+3
4
1
Y=- x–5
4
5
5
Y= x+
3
3
y=
y = -4x + 9
y = 4x + 9