CC Geometry R
Aim #7: How do dilations map circles?
Do Now:
1) When a dilation is performed on a hexagon, which property of the hexagon will
not be preserved in its image?
(1) parallelism
(3) orientation
(2) length of sides
(4) measure of angles
2) Under a dilation, the image of A(3,6) is A‛(4, 8). What is the scale factor for
the dilation? __________
3) For each case below, will a dilation about center O and scale factor r = 1 map
PQ to P'Q'? Explain.
a)
b)
Q
Q
P
P
O
O
1. Using your ruler, perform the dilation DO,1.5 on circle O.
O
2. Using your ruler, perform the dilation DP,2 on circle O.
P
O
3. Dilate circle O by a scale factor r = 1/2 using a compass. The center of
dilation is the center of the circle.
O
4. The larger circle is a dilation of the smaller circle. Find the center of dilation O. (Hint:
determine where point A would lie on circle C. From the dilation theorem, we know what
C'A' || CA. )
C'
C
A'
5. The diagram below shows the dilation of circle C with center O and radius R. A
dilation with center D was performed using scale factor r. Find point W on circle C
that is mapped to point W' on circle C'.
OW ____O'W'
6. Using your compass, dilate circle C with radius CA from center O with a scale
factor r = 2.
O
C
7. The larger circle is a dilation of the smaller circle. Find the center of dilation O.
8. Will a dilation about a center O and scale factor r map a given circle with
a given radius onto another circle?
Circle A' is a dilation of circle A using the
origin as the center of dilation.
What is the scale factor?
A"
A
Circle A" is a dilation of A' using the origin
as the center of dilation.
What is the scale factor for the dilation
of Circle A onto Circle A"?
A'
Dilate circle A' using a scale factor of 1.5.
Let's Sum it Up!
Will a dilation about a center O and scale factor r map a circle of radius R
onto another circle?
Examine the case where the center of the dilation coincides with the center
of the circle. Let C be a circle with center O and radius R.
If the center of the dilation is also O, then every point P on the circle is
sent to P' on OP so that OP' = _____ x _____ or ______ x _______.
R= radius
C'
P'
C
r = scale factor
P
}
O
R
A dilation moves every point on the circle toward or away from the center the
same amount so the dilated image is still a circle. Circles that share the same
center are called _________________ ___________________.