Question

12. Algebra Two similar figures are similar based on

the transformation (x, y) → (12x, 3a’y). What is/
are the value(s) of a?

Answer 1

The transformation (x, y) → (12x, 3a’y) can be compared to the standard similarity transformation to determine the value of a, which is 4.

Step-by-step explanation:

The given transformation is (x, y) → (12x, 3a’y). To determine the value of a, we need to compare the transformation with the standard similarity transformation, which is (x, y) → (kx, ky), where k is the scale factor.

Comparing the two transformations, we can equate the corresponding components:

12x = kx

3a’y = ky

Simplifying the equations, we get:

k = 12

3a’ = k

Substituting the value of k, we have:

3a’ = 12

a’ = 4

Therefore, the value of a is 4.

Answer 2

• a = ± 2

Step-by-step explanation:

Let the scale factor is k.

Then the transformation is:

• (x, y) → (kx, ky)

We have:

• (x, y) → (12x, 3a²y)

The scale factor is k = 12, find the value of a:

• 3a² = 12
• a² = 4
• a = √4
• a = ± 2