Question

triangle abc has been transformed into triangle abc. the algebraic formula for this transformation is
a ((x, y) = (2x, y))
b ((x, y) = (x, 2y))
c ((x, y) = (2x, 2y))
d ((x, y) = (2y, 2x))
e ((x, y) = (-2x, y))

Explanation:

Step1: Identify coordinates of ABC

Let's find coordinates of triangle ABC. From the graph, assume:

• A: (-1, -2)
• B: (-1, 2)
• C: (2, 1)

Step2: Identify coordinates of A'B'C'

Now coordinates of A'B'C':

• A': (-2, -4)
• B': (-2, 4)
• C': (4, 2)

Step3: Analyze transformation

Check each option:

• Option A: (2x, y). For A(-1,-2): (2*(-1), -2)=(-2,-2) ≠ A'(-2,-4). Eliminate.
• Option B: (x, 2y). For A(-1,-2): (-1, 2*(-2))=(-1,-4) ≠ A'(-2,-4). Eliminate.
• Option C: (2x, 2y). For A(-1,-2): (2(-1), 2(-2))=(-2,-4) (matches A'). For B(-1,2): (2(-1), 22)=(-2,4) (matches B'). For C(2,1): (22, 21)=(4,2) (matches C'). This works.
• Option D: (2y, 2x). For A(-1,-2): (2(-2), 2(-1))=(-4,-2) ≠ A'(-2,-4). Eliminate.
• Option E: (-2x, y). For A(-1,-2): (-2*(-1), -2)=(2,-2) ≠ A'(-2,-4). Eliminate.

Answer:

C. \((x', y') = (2x, 2y)\)