Final Answer:
The value of A, B and C reflected across the x-axis is c) A'(-2, -1), B'(-4, -6), C'(-8, -4)
Step-by-step explanation:
To reflect points across the x-axis, we invert the sign of the y-coordinates while keeping the x-coordinates unchanged. For point A(2, 1), the reflected point A' is obtained by changing the sign of the y-coordinate, resulting in A'(-2, -1). Similarly, for point B(4, 6), the reflected point B' is B(4, -6), and for point C(8, 4), the reflected point C' is C(-8, -4).
This reflection process is based on the symmetry of the x-axis. When a point is reflected across the x-axis, its distance from the x-axis remains the same, but the sign of the y-coordinate changes. This is a fundamental property of geometric transformations.
In mathematical terms, if a point is represented as (x, y), its reflection across the x-axis is given by (x, -y). Therefore, to find the reflected points A', B', and C', we apply this transformation to the original coordinates, yielding A'(-2, -1), B'(-4, -6), and C'(-8, -4). This corresponds to option c) in the given choices.