Pre-Algebra Intervention: Dilations

Dilations

by Matthew Taylor

One quick thing before we begin.

​We need to identify which shape is the ORIGINAL and which shape is the IMAGE (the new shape).

​

​The ORIGINAL will just have letters like A B and C.

​

​The IMAGE will have primes (they look like this ' ) So for example, A' B' and C'

​Steps to writing an Algebraic Rule for Dilations

Multiple Choice

Triangle E’F’G’ is a dilation of triangle EFG.

Which rule best represents the dilation shown?

• (x, y) --> (2x, 2y)

• (x, y) --> (0.5x, 0.5y)

• (x, y) --> (x + 2, y - 2)

• (x, y) --> (2x, 0.5y)

Multiple Choice

Trapezoid A’B’C’D’ is the dilation of trapezoid ABCD.

Which algebraic representation shows this dilation?

• (x, y) --> (2x, 2y)

• (x, y) --> (0.5x, 0.5y)

• (2x, 2y) --> (x, y)

• (x, y) --> (3x, 2y)

Multiple Choice

Triangle ABC is dilated by a scale factor of one-half to form Triangle A’B’C’ with the origin as a center of dilation.

Which rule represents this dilation?

• (x, y) --> (2x, 2y)

• (x, y) --> (1/2x, 1/2y)

• (2x, 2y) --> (x, y)

• (x, y) --> (1/3x, 1/3y)

Multiple Choice

Quadrilateral WXYZ was dilated with the origin as the center to create quadrilateral W’X’Y’Z’.

Which rule best represents the dilation that was applied to quadrilateral WXYZ to create quadrilateral W’X’Y’Z’?

• (x, y) --> (0.4x, 0.4y)

• (x, y) --> (x + 3, y + 2)

• (x, y) --> (2.5x, 2.5y)

• (x, y) --> (x - 3, y - 2)

​Enlargements

​You may have noticed a pattern when it comes to the "k" value and the size of the transformation.

​

​When k is bigger than 1, the new shape is larger. This means that when k is greater than 1, we have an enlargement.

​Reductions

​When k is less than one, we may have noticed that the Image is smaller than the original. This means that when k is less than 1 it is a reduction.

Multiple Choice

Is this an enlargement or a reduction?

• Enlargement

• Reduction

Multiple Choice

Is this an enlargement or a reduction?

• Enlargement

• Reduction

Multiple Choice

Is this an enlargement or a reduction?

• Enlargement

• Reduction

Multiple Select

Which of the following algebraic rules represents an enlargement?

• (x, y) --> (3x, 3y)

• (x, y) --> (0.5x, 0.5y)

• (x, y) --> (0.75x, 0.75y)

• (x, y) --> (0.999x, 0.999y)

• (x, y) --> (5x, 5y)

Multiple Select

Which of the following algebraic rules represents a reduction?

• (x, y) --> (3x, 3y)

• (x, y) --> (0.5x, 0.5y)

• (x, y) --> (0.75x, 0.75y)

• (x, y) --> (0.999x, 0.999y)

• (x, y) --> (5x, 5y)

Poll

How do you feel about dilations?

• I feel GREAT!

• I feel A'ight!

• I am worried about this.

• Please Help!