Hi there!
The answer to your question is B my explanation is below
The coordinates of the vertices of the final image will be:
A''(-6, 8), B''(-7, -2), and C''(0, -2)
Hence, option (B) is true.
Step-by-step explanation:
Given the triangle with the vertices
A(-1, -8)B(-2, 2)C(5, 2)We know that when we reflect a point across the x-axis, the x-coordinate remains the same, but the y-coordinate reverses its sign.
Thus,
The rule of reflection across the x-axis:
(x, y) → (x, -y)
so
A(-1, -8) → A'(-1, -(-8)) = A'(-1, 8)
B(-2, 2) → B'(-2, -2) = B'(-2, -2)
C(5, 2) → C'(5, -2) = C'(5, -2)
Then, translate the new triangle 5 units to the left
Rule of translating 5 units to the left
(x, y) → (x-5, y)
so
A'(-1, 8) → A''(-1-5, 8) = A''(-6, 8)
B'(-2, -2) → B''(-2-5, -2) = B''(-7, -2)
C'(5, -2) → C''(5-5, -2) = C''(0, -2)
Therefore, the coordinates of the vertices of the final image will be:
A''(-6, 8), B''(-7, -2), and C''(0, -2)
Hence, option (B) is true.
