22 Aug 2016 8:00 - 9:30 AM
Geometry Proposed Agenda
Bulletin - (remember you can always go to Clarkmagnet.net
to read the night before school)
Review Transformational Geometry for Quiz on
Wednesday
Slope and distance formula (p. 17 and 17b)
Homework
Translation
any shape
T4, -2
S
What are the
key things to
know?
x-axis
Translation
any shape
T4, -2
S
’
Move x
first
y next
x-axis
Translation
any shape
T4, -2
S
’
All
points
on
shape,
move
same
x-axis
congruent
original and
image shape
Reflection any
shape
ry=3
S
What are the
key things to
know?
x-axis
Reflection any
shape
ry=3
S
S
’
Where line of
reflection is.
x-axis
T
R (O, 90°)
S
R(2, 3)
R’( )
R
R’
What are the
key things to
know?
x-axis
T
b) R (O, 90°)
Counter
clockwise
R’
R(2, 3)
R’( )
S
R
x-axis
T
b) R (O, 90°)
S
R(2, 3)
R’(-3, 2)
R
R’
x-axis
T
S
R
b) R (O, 90°)
S(5, 4)
S’( )
R’
x-axis
T
S’
S
R
b) R (O, 90°)
S(5, 4)
S’( )
R’
x-axis
T
S’
S
R
b) R (O, 90°)
S(5, 4)
S’(-4, 5)
R’
x-axis
T
S’
S
R
R’
x-axis
b) R (O, 90°)
T (4, 8)
T’(
)
T
S’
S
R
R’
x-axis
b) R (O, 90°)
T (4, 8)
T’(-8, 4)
T
S’
S
R
R’
x-axis
b) R (O, 90°)
T (4, 8)
T’(-8, 4)
T
Composite
T -2, 4 o R (O, 270°)
R
What are the
key things to
know?
x-axis
T
Composite
T -2, 4 o R (O, 270°)
R
R’
Work from
right to left like
for functions
g[f(x)]
x-axis
Geometry: Vocabulary Review
△ABD is a triangle (pick a direction & go)
△ABC
△BCD
Geometry: Vocabulary Review
ACB is a right angle
DCB is a right angle
Geometry: Vocabulary Review
CB is a ray
AD is a ray
Any others?
Geometry: Vocabulary Review
A, B, C, and D are all points
Geometry: Vocabulary Review
AB is a line segment
Any others?
Geometry: Vocabulary Review
DAB is an obtuse angle (greater than 90°)
Any others?
Geometry: Vocabulary Review
And
are supplementary angles
Geometry: Vocabulary Review
DAB And
angles
BAC
are supplementary
(add up to 180°)
Any others?
Geometry: Vocabulary Review
CB
CD (perpendicular lines)
Geometry: Vocabulary Review
CB
|
CD (perpendicular lines)
Apologies for the funny double headed
arrows above the letters - closest I got
today for notation for a line!
Transformations Quiz: Wednesday
Bring work booklet (to work in if needed) and
the Review packet (to turn in).
4 transformations questions.
“Label each figure, the first one has been done
for you. Write the coordinates in the space
provided. Draw the correct translated figure
(A’B’C’D’) on each grid and write the
coordinates in the space.
For example
a) R(Origin, 180°)
A( , ) →
B( , ) →
C( , ) →
D( , ) →
show your thinking on the grid
A’( , )
B’ ( , )
C’( , )
D’( , )
Slope and Distance Formula p. 17
1) Plot the two points listed below to create
the line segment AB.
A(-3, 4) B(5, -1)
2) Find the slope (m) between the two lines.
Slope is a rate of change
Rise (change in y) over
run (change in x)
A
-5
C
Negative slope here
8
B
Slope is a rate of change
Rise (change in y) over
run (change in x)
A
5
C
Negative slope here
8
B
m = -5
8
Slope and Distance Formula p. 17
3) How could we have found the slope
between A and B without graphing the two
points?
A(-3, 4) B(5, -1)
Change in y
Change in x
Slope and Distance Formula p. 17
3) How could we have found the slope
between A and B without graphing the two
points?
A(-3, 4) B(5, -1)
Change in y = (-1 - 4) = -5
Change in x
5 - -3
8
Slope and Distance Formula p. 17
3) How could we have found the slope
between A and B without graphing the two
points?
A(-3, 4) B(5, -1)
Change in y = (-1 - 4) = -5
Change in x
5 - -3
8
4) Using the Pythagorean Theorem, find the
distance between points A and B.
The square on the hypotenuse is equal to the
sum of the squares on the other two legs.
A
Pythagorean theorem for
c
b
B
c2 = a 2 + b 2
C
a
In our situation:
AB2 = (-5)2 + (8)2
4) Using the Pythagorean Theorem, find the
distance between points A and B.
The square on the hypotenuse is equal to the
sum of the squares on the other two legs.
A
Pythagorean theorem for
c
b
B
c2 = a 2 + b 2
C
a
In our situation:
AB2 = (-5)2 + (8)2
AB2 = (25 + 64)2
AB = 89
5) How does the process you used to find the
slope in #2 relate to how you found the distance
between A and B in #3?
Explain.
5) How does the process you used to find the
slope in #2 relate to how you found the distance
between A and B in #3?
Explain.
The rise (which was a fall in this case of 5 units,
or -5 in the y direction on the grid) and run (how
much x changed, 8 units) were the legs of the
right triangle and so the sum of their squared
values gave the square on the hypotenuse of the
right triangle which was the length AB.
6) Find the slope between the points and the
distance between them.
C(4, 5) D(-1, 2)
m= 2-5
=-3 =3
-1 - 4
-5 5
CD2 = (3)2 + (5)2
CD2 = (9 + 25)2
CD =
34
7) Find the slope between the points and the
distance between them.
P(x1,y1) Q(x2, y2)
m = y 2 - y1
x2- x1
PQ = (y2 - y1)2 + (x2- x1)2
Practice (bottom page 17)
1) Find the slope between the points and the
distance between them. E(-3,5) F(5, 3)
m = (3 - 5) = - 2 = - ¼ negative slope, simplified
5 - (-3) 8
Distance = (-2)2 + 82
=
68 = 2 17
Practice (bottom page 17)
2) Find the slope between the points and the
distance between them. G(8, -3) and H(-5, -4)
m = (-4 - -3) = - 1 = 1 positive slope
-5 - 8
-13 13
Distance = 12 + 132
=
170
Carry on practicing using:
Distance Formula Homework (p. 17b) page.
Do All the problems.
Show your work and explain your thinking.
Note that A must be (-1, 2)
Distance Formula Homework (p. 17b) page.
Do All the problems. - we checked 1-4 in class.
5. I helped you with the diagram.
Distance = 1700 = 100(17) = 10 17
Show your work and explain your thinking.
Note that A must be (-1, 2)
Distance Formula Homework (p. 17b) page.
Do All the problems. - we checked 1-4 in class.
5. I helped you with the diagram.
Distance = 1700 = 100(17) = 10 17
Show your work and explain your thinking.
Homework - for today and Wed.
Study/ prepare for Transformations Quiz
on Wednesday Aug 24th.
Do Distance Formula Homework (p 17b)
Question 6 on Separate graph paper and I will
collect that on Friday. Show all your work.
Note that point A should be (-1, 2)