Transcript B - grantham7

List the coordinates for the following:
H
M ____
L
I
C
(-7,-2)
(-7,-5)
A ____
D
O
(-7, 5)
T ____
T
(-9, 9)
F
N
X
B
U
G
H ____
( 5, 9)
I ____
Y
W
(-7,-8)
S ____
M
Q
J
A
E
( 9, 4)
F ____
R
( 0, 0)
V
S
P
K
Z
U ____
(-3, 3)
N ____
A coordinate plane is a way to locate points in a plane. A point in a
plane can be located by its distances from both a horizontal and a
vertical line called the axes. The horizontal line is called the x-axis,
and the vertical line is called the y-axis. The axes separate the
coordinate plane into four quadrants.
The pairs of numbers are called ordered pairs. The first number is
the x-coordinate, and the second number is the y-coordinate.
The point at which the two axes intersect is called the origin. (0,0).
In general, coordinates are written:
(x, y)
Start at the origin. The x-coordinate tells you how
many places to move right (+) or left (-). The ycoordinate tells you how many places to then move up (+)
or down (-).
What are the
coordinates for
point A and B?
What quadrant
are they in?
A
B
What point lies at the coordinates (-3, 2)?
A
C
B
D
What point has the coordinates (-3.5, 6 ½ )?
A
B
D
C
What point lies halfway between point A and the y-axis?
C
A
B
When you are sliding down
a water slide, you are
experiencing a
translation. Your body is
moving a given distance
(the length of the slide) in
a given direction. You do
not change your size, shape
or the direction in which
you are facing.
Translations can be seen in wallpaper designs, textile
patterns, mosaics, and artwork.
The famous artist M. C. Escher continually
used translations, reflections, and rotations in his art
work.
A translation is a slide. Each of the points of the
geometric figure move the same distance in the same
direction. The new points are called images of the
original points. We show the image, or the new
points with the apostrophe symbol. Ex. A’,B’,C’
A
C
B
D
A’
C’
B’
D’
In the example below, notice how each vertex moves the same
distance in the same direction.
In this next example, the "slide" moves the figure
7 units to the left and 3 units down
How did each of the points slide to form the new image of
trapezoid ABCD?
A
C
B
D
A’
C’
B’
D’
Which rule was applied to translate Figure A
to create Figure A as shown below?
A
A’
A)( x  6, y  7)
B )( x  6, y  5)
C )( x  6, y  7)
D )( x  7, y  6)
A reflection is a transformation that flips a figure
over a line. That line is called the line of reflection.
In the diagram below, D and D’, are the same
distance from the line of reflection, or the y-axis.
A
C
B
D
C’
D’
A’
B’
If a figure can be reflected over a line so its image matches the
original figure, the figure has reflectional symmetry. The line that
divides the figure into mirror images is called a line of symmetry.
line of symmetry
Reflecting over the x-axis:
When you reflect a point across the x-axis, the xcoordinate remains the same, but the y-coordinate is
transformed into its opposite.
The reflection of the point (x,y) across the x-axis is
the point (x,-y).
A
A’
Hint: If you forget this "rule", simply fold your graph paper along the x-axis
to see where your new figure will be located. You can also measure how far
your points are away from the axis as indicated in the picture above.
Reflecting over the y-axis:
When you reflect a point across the y-axis, the
y-coordinate remains the same, but the xcoordinate is transformed into its opposite.
The reflection of the point (x,y) across the yaxis is the point (-x,y).
A
A’
Find the coordinates of A if the figure below is reflected over the x-axis.
A
1
1
A)( 5 ,3 )
2
2
1 1
C )( 5 ,3 )
2 2
1 1
B)(3 ,5 )
2 2
1
1
C )(3  5 )
2,
2
You are probably familiar with the word "dilate" as
it relates to the eye. "The pupils of the eye were
dilated." As light hits the eye, the pupil enlarges or
contracts depending upon the amount of light. This
concept of enlarging and contracting is "dilating".
A dilation is a transformation that produces an image
that is the same shape as the original, but is a
different size. A dilation used to create an image
larger than the original is called an enlargement. A
dilation used to create an image smaller than the
original is called a reduction.
If the scale factor, or number that we are
multiplying by to get the new coordinates, is greater
than 1, the image is an enlargement. If the scale
factor is between 0 and 1, the image is a reduction.
A figure and its dilation are similar figures.
OBSERVE: Notice how
EVERY coordinate of the
original triangle has been
multiplied by the scale
factor (x2).
HINT: Dilations involve
multiplication!
OBSERVE:
Notice how
EVERY coordinate
of the original
pentagon has been
multiplied by the
scale factor (1/3).
HINT:
Multiplying by 1/3
is the same as
dividing by 3!
2
If the figure below is dilated using a scale factor of ,
3
what will be the coordinates of A’?
A
2 2
(2 , )
3 3
2
If the figure below is dilated using a scale factor of ,
1
what will be the coordinates of A’?
A
(2,2)
A rectangle is shown on the grid.
5
4
3
2
1
-4 -3 -2 -1 0
1
-1
L -2
-3
8
M -4
2
3
4
5
O
N
What would be the new coordinates of vertex L if the rectangle is
translated so that the new coordinates of vertex N are (1,1)?
A)
(1,3)
C)
(-4,3)
B)
(3,-4)
D)
(-4,1)
A triangle is shown on the grid.
5
4
3
2
1 G
I
-4 -3 -2 -1 0
1
-1
-2
-3
8
-4
H
2
3
4
5
What would be the new coordinates of vertex G if the triangle is
translated so that the new coordinates of vertex I are (0,3)?
A)
(1,0)
C)
(4,-3)
B)
(-3,4)
D)
(0,1)
Using the y-axis as a line of symmetry, identify the
reflection of point Z.
A. (2,-2)
B (2,2)
C (-2,-2)
D (0,2)
If point A is translated five units in the positive direction
along the line y=2, what will be its new location?
A. (-3,7)
B (-8,2)
C (-3,-3)
D (2,2)
If the figure is reflected over the x-axis, the new
coordinates of the vertices will be (2,-2), (4,-2), and --
A. (-4,-3)
B (-4,2)
C (2,-4)
D (3,-4)
If the figure is translated over the y-axis, the new
coordinates of the vertices will be (-5,4), (-2,4), (-5,3),
and --
A. (-3,3)
B (-2,-3)
C (-2,3)
D (-4,2)
If the figure is reflected over the x-axis, the new
coordinates of the vertices will be (-2, -5), (-2,-3), (-5,-5),
and --
A. (5,-3)
B (-3,-5)
C (-5,-3)
D (-2,5)
If the figure is reflected over the y-axis, the new
coordinates of the vertices will be (1,5), (2,3), (5,5),
and --
A. (5,5)
B (2,5)
C (5,3)
D (4,3)
A translation moves the point K(1, -9)
to an image point K’(8, -6). Explain
how to determine the rule for this
translation.