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Aim #2: How do we create scale drawings using the ratio method?
Do Now:
1. Figure
CC Geometry H
I has been dilated to create figure II. What
conclusion can you make about the numerical value of the
scale factor?
I
II
I
II
2. Figure I has been dilated to create figure II. What
conclusion can you make about the numerical value of the
scale factor?
Notes about dilations:
1. A dilation moves points a specific distance along a ray from a center O. The
location of the scaled point is determined by a _________ __________ (r) and
the distance of the original point from the center.
2. The scale factor for a dilation where a point is pulled towards the center must
be ____ < r < ____.
3. The scale factor for a dilation where a point is pushed away from the center
must be r > ___.
4. A point (other than the center) that is unchanged in its location after a
dilation must have scale factor r = ____.
5. A scale factor, r, is always a __________________ number.
6. DO,r represents a dilation using center O and scale factor r.
The ratio method creates a scale drawing, given center O and scale factor r. The
ratio method dilates each vertex of the provided polygonal figure. To apply the
ratio method:
1. Use your ruler to draw a ray from O, passing through each vertex of the figure.
2. Measure the distance between O and a vertex, and multiply it by the scale
factor. The resulting value is the distance away from O at which the scaled
point will be located.
3. Once all the vertices are dilated, join them in the order of the original figure.
4. To determine whether the scale drawing is correctly done, use a ruler
to measure the side lengths of the pre-image and image and a
protractor to measure corresponding angles. If the side lengths are in
constant proportion and the corresponding angles are equal, the new figure
is a correct scale drawing of the original.
1) Use the ratio method to create a scale drawing of the figure below given center
C and scale factor 2.
a) What does the scale factor tell us about the distance of each scaled point from
C? ___________________________________________________________
_____________________________________________________________
b) Using a ruler and measuring in mm, locate points R', S', and T'.
c) Verify that the resulting figure is a scale drawing by showing the corresponding
side lengths are in constant proportion and the corresponding angles are equal in
measure. (Use ruler and protractor.)
2) Use the ratio method to create a scale drawing of the figure below given center
1
O and scale factor /2.
a) What does the scale factor tell us about the distance of each scaled point from
O? ___________________________________________________________
______________________________________________________________
b) Using a ruler and measuring in mm, locate points A', B', C', D' and E'.
D
E
C
A
B
O
3) ΔA'B'C' is a scale drawing of ΔABC drawn by using the ratio method. Use
your ruler to determine the location of the center O used in the scale drawing.
4) a) Using the ratio method, create a scale drawing of the figure below with
center O and scale factor r = 3.
D
B
A
C
O
b) How can we verify that A'B'C'D' is a correct scale drawing of ABCD?
c) Locate a point X so that it lies between endpoints A and B on segment AB in
the figure above. Use the ratio method to locate X' on the scale drawing. All
points between A and B are dilated to corresponding points between ___ and
____.
Name ________________________
Date __________________
CC Geometry H
HW # 2
1) Use the ratio method to create a scale drawing about center O with a scale
factor of r = 1/4. Use a ruler and protractor to verify that the resulting figure
is in fact a scale drawing by showing the corresponding side lengths are in
constant proportion and the corresponding angles are equal in measurement.
D
O
A
B
C
2) Use the ratio method to create a scale drawing about center O with a scale
factor of r = 2. Verify that the resulting figure is in fact a scale drawing by
showing that corresponding side lengths are in constant proportion and that the
corresponding angles B and B' and C and C' are equal in measurement.
A
B
D
O
C
OVER
3) Use the ratio method to create two scale drawings: DO,2 and DP,2. Label the
scale drawing with respect to center O as ΔA'B'C' and the scale drawing with
respect to center P as A"B"C".
C
A
B
P
O
What do you notice about the two scale drawings? _____________________
Mixed Review
1) Construct a line perpendicular to the given line m through the given point P:
m
P
2) In parallelogram PQRS, the ratio of the m≮Q to the m≮R is 1:5. Find m≮Q.
o
3) In rectangle ABCD, diagonal AC is drawn. If the m≮DCA = 30 , find the measure
of m≮CAD.