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Dilations on a Coordinate Plane

Learn what dilations are, how they change object sizes, and how to calculate dilated coordinates with examples and step-by-step instructions.

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Dilations on a Coordinate Plane

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  1. Dilations on a Coordinate Plane

  2. Definition • Dilation changes the size of an object without changing the shape. Examples of dilation: • Your eyes • Enlarging or reducing a picture

  3. Dilation Rule • To dilate a figure with respect to the origin, multiply the coordinates of each of its points by the percent of dilation. (2x, 2y)

  4. Steps • Find the proper multiplier. Hint: change percent to a decimal - A 150% dilation would be a 1.5 multiplier. • Find the coordinates of each vertex by multiplying the original coordinates by the multiplier.

  5. Example Quadrilateral ABCD has vertices A(-2,0), B(-2,4), C(2,6), and D(6,-2). Find the new coordinate of 150% dilation. • Multiplier: Change 150% to decimal 1.5 • Multiply all coordinate by 1.5 A: -2 × 1.5 = -3 0 × 1.5 = 0 A’(-3,0) B: -2 × 1.5 = -3 4 × 1.5 = 6 B’(-3,6) C: 2 × 1.5 = 3 6 × 1.5 = 9 C’(3,9) D: 6 × 1.5 = 9 -2 × 1.5 = -3 D’(9,-3)

  6. Example: Making the figure bigger. • PROBLEM:  Draw the dilation image of triangle ABC with the center of  dilation at the origin and a scale factor of 2. • OBSERVE: Notice how EVERY coordinate of the original triangle has been multiplied by the scale factor (x2). • HINT: Dilations involve multiplication!

  7. Example: Making the figure smaller. • PROBLEM:  Draw the dilation image of pentagon ABCDE with the center of  dilation at the origin and a scale factor of 1/3. • OBSERVE: Notice how EVERY coordinate of the original pentagon has been multiplied by the scale factor (1/3). • HINT: Multiplying by 1/3 is the same as dividing by 3!

  8. Practice 1.Draw ∆ABC after a dilation of 3. A(1,3) B(4,3) C(4,1) 2. Draw ∆DEF after a dilation of 1/2 D(2,2) E(2,6) F(6,4)

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