Identify and draw dilations

1. Coordinates and Proportions
The student is able to (I can):
• Identify and draw dilations
• Identify scale factors and use scale factors to solve
problems

2. Scale factor and coordinates:
What point is the image of A under the
dilation with the given scale factor with the
center of dilation at 0?
1. k = 2
2(2) = 4, thus point D
2. k = −1
2(−1) = −2, thus point B
3. k =
| || ||| | ||
0 2 4-2-4
••• •
AB C D
1
2
−
1
2 1, thus point C
2
 − = − 
 

3. If P(x, y) is a point being dilated centered
at the origin, with a scale factor of k, then
the image of the point is P´(kx, ky).
Example: What are the coordinates of a
triangle with vertices S(−3, 2), K(0, 4), and
Y(2, −3) under a dilation with a scale
factor of 3, centered at the origin?
S´(3(−3), 3(2)) = S´(−9, 6)
K´(3(0), 3(4)) = K´(0, 12)
Y´(3(2), 3(−3)) = Y´(6, −9)
Note: If k is negative, the resulting dilation
will be rotated 180º about the center.

4. Examples Dilate the following vertices by the given
scale factor. All dilations are centered
about the origin.
1. B(2, 0), I(3, 3), G(5, −1); k=2
B´(4, 0), I´(6, 6), G´(10, −2)
2. T(-3, -3), I(-3, 3), N(6, 3), Y(6, -3); k=
T´(-1, -1), I´(-1, 1), N´(2, 1), Y´(2, -1)
3. S(−4, 2), E(−6, 0), A(−2, −4); k=
S´(2, −1), E´(3, 0), A´(1, 2)
1
3
1
2
−