Answer:
Option C is the right option. i.e. you can map ΔABC onto ΔA'B'C' by reflecting it over the x-axis and translating it 7 units right, which is a sequence of rigid motions.
Step-by-step explanation:
As the ΔABC has the vertices A, B and C,
The vertex A has the coordinates (3, 5)
The vertex B has the coordinates (-2, 3)
The vertex C has the coordinates (-4, -1)
And the congruent ΔA'B'C' has the vertices
A''(10, -5)
B''(5, -3)
C''(3, 1)
The rule of reflection across x-axis states that a point (x, y) will transform into (x, -y) when you reflect a point across x - axis, meaning the x-coordinate remains same, but y-coordinate changes its sign.
So, after reflection across x-axis,
A(3, 5) ⇒ A'(3, -5)
B(-2, 3) ⇒ B'(-2, -3)
C(-4, -1) ⇒ C'(-4, 1)
The rule of translation a unit to the right states that when if we move horizontally one units to the right, 1 is added to the x-coordinate of each of the vertices. In other words, (x, y) → (x + 1, y)
So, Translation 7 units to the right.
(x, y) → (x + 7, y)
So, after translating 7 units to the right
A'(3, -5) ⇒ A''(10, -5)
B'(-2, -3) ⇒ B''(5, -3)
C'(-4, 1) ⇒ C''(3, 1)
So, compare the results and check that the transformed triangle ΔA'B'C' as shown in figure with the coordinates A'(10, -5), B'(5, -3), C'(3, 1) is having the same coordinates what we achieved in following the sequence of first reflecting across x-axis and then translating 7 units to the right.
i.e. A''(10, -5), B''(5, -3), C''(3, 1) = A'(10, -5), B'(5, -3), C'(3, 1)
So, we can safely say that option C is the right option i.e. you can map ΔABC onto ΔA'B'C' by reflecting it over the x-axis and translating it 7 units right, which is a sequence of rigid motions.
