Dilations on the Coordinate Plane

Name ______Module 2

Dilations on the Coordinate Plane

Learning Target: I can perform dilations on the coordinate plane.

Opening Exercises

1. A. What are the coordinates of ∆PQR?

B. Multiply each coordinate of each vertex by 2. Graph this image and label it ∆P'Q'R'.

2. A. What are the coordinates of ∆PQR?

B. Multiply each coordinate of each vertex by 12. Graph this image and label it ∆P'Q'R'.

3. ∆JKL is the image of ∆ABC after a dilation. Determine the scale factor and the length of JK.

Dilations on the Coordinate Plane

A dilation is a transformation that changes the size of a figure but not its shape. The preimage and the image are always similar. A scale factor describes how much the figure is enlarged or reduced. For a dilation with scale factor k, you can find the image of a point by multiplying each coordinate by k: (a, b) ® (ka, kb).

1. A. Graph, label and state the coordinates of ∆A'B'C', the image of ∆ABC after the dilation D2.

B. Graph, label, and state the coordinates of ∆A''B''C'', the image of ∆A'B'C' after the dilation D-1.

The following three transformations result in the same image:

·  Dilation of –1 (D-1)

·  Rotation of 180o about the origin (R180)

·  Point reflection in the origin (rO)

2. Graph the image of ∆ABC after a dilation with scale factor 23 and state its coordinates.

3. A. Graph, label and state the coordinates of ∆PQR with vertices P(–4, 4), Q(–2, –2), and R(4, 0).

B. Graph, label and state the coordinates of ∆P'Q'R', the image of ∆PQR under a dilation with a

scale factor of 12 centered at the origin.

4. What are the coordinates of the point (6, –14) under the dilation D-3?

5. The image of point A after a dilation of 4 is (8, 24). What was the original location of point A

6. The point P(20, 15) maps onto P’(4, 3) under a dilation with respect to the origin. What is the constant of dilation?

Name ______Module 2

Dilations on the Coordinate Plane Problem Set

1. What is the image of point A(1,3) after a dilation with the center at the origin and a scale factor of 4?

2. If P(4,-3) is transformed under the dilation D-2, what are the coordinates of P'?

3. In which quadrant would the image of point (5,-3) fall after a dilation using a factor of -3?

4. The image of point A after a dilation of 3 is (6,15). What was the original location of point A?

5. If the image of A after a dilation of -2 is A'(-8,6), what are the coordinates of A?

6. The point A(6,3) maps onto A'(18,9) under a dilation with respect to the origin. What is the constant of dilation?

7. Under a dilation with respect to the origin, the image of P(-15,6) is P'(-5,2). What is the constant of dilation?

8. If the dilationDk-2,4 equals (1,-2), the scale factor k is equal to

9. Under a dilation where the center of dilation is the origin, the image of A(-2,-3) is A'(-6,-9). What are the coordinates of B', the image of B(4,0) under the same dilation?

10. Which transformation represents a dilation?

1) /
2) /
3) /
4) /

11. On the accompanying set of axes, graph ∆ABC with coordinates A(-1,2), B(0,6), and C(5,4). Then graph ∆A'B'C', the image of ∆ABC after a dilation of 2.

Name ______Module 2

Dilations on the Coordinate plane Exit Ticket

On the accompanying grid, graph and label quadrilateral ABCD, whose coordinates are A(-1,3), B(2,0), C(2,-1), and D(-3,-1). Graph, label, and state the coordinates of A'B'C'D', the image of ABCD under a dilation of 2, where the center of dilation is the origin.