1. 9-7
Dilations
Holt McDougal Geometry
Holt Geometry

2. Warm Up
1. Translate the triangle with vertices A(2, –1), B(4, 3), and C(–5, 4) along the vector <2, 2>.
2. ∆ABC ~ ∆JKL. Find the value of JK.

3. A dilation is not considered an isometry.
Recall that a dilation is a transformation that changes the size of a figure but not the shape.
A dilation is not considered an isometry.
The image and the preimage of a figure under a dilation are similar.
A dilation enlarges or reduces all dimensions proportionally. A dilation with a scale factor greater than 1 is an enlargement, or expansion. A dilation with a scale factor greater than 0 but less than 1 is a reduction, or contraction.

4. Tell whether each transformation appears to be a dilation. Explain.

6. On a sketch of a flower, 4 in. represent 1 in. on the actual flower
On a sketch of a flower, 4 in. represent 1 in. on the actual flower. If the flower has a 3 in. diameter in the sketch, find the diameter of the actual flower.

7. An artist is creating a large painting from a photograph into square and dilating each square by a factor of 4. Suppose the photograph is a square with sides of length 10 in. Find the area of the painting.

8. For a dilation with scale factor k, if k > 0, the figure is not turned or flipped. If k < 0, the figure is rotated by 180°.
Helpful Hint

9. If the scale factor of a dilation is negative, the preimage is rotated by 180°. For k > 0, a dilation with a scale factor of –k is equivalent to the composition of a dilation with a scale factor of k that is rotated 180° about the center of dilation.

10. Draw the image of the triangle with vertices
P(–4, 4), Q(–2, –2), and R(4, 0) under a
dilation with a scale factor of centered at the origin.

11. Lesson Quiz
1. Tell whether the transformation appears to be a dilation.
2. A rectangle on a transparency has length 6cm and width 4 cm and with 4 cm. On the transparency 1 cm represents 12 cm on the projection. Find the perimeter of the rectangle in the projection.

12. 3. Draw the image of the triangle with vertices
E(2, 1), F(1, 2), and G(–2, 2) under a dilation with a scale factor of –2 centered at the origin.