Final answer:
The coordinates of the point J' to produce a congruent triangle J'K'L' after a 90-degree clockwise rotation cannot be accurately determined without the original position of J. However, Option 1 cannot be dismissed based on the given rotation point.
Step-by-step explanation:
To determine the coordinates of point J' such that triangle J'K'L' is congruent to triangle JKL after a 90 degrees clockwise rotation around the point (1, -6), we must consider the properties of rotation. By rotating a point 90 degrees clockwise, the coordinates (x, y) transform into (y + h, -x + k) where (h, k) is the rotation point. Since no starting coordinates for point J are given, we can only infer its new position relative to the rotation point.
If we apply these transformations to an unknown point J(x, y) about the center of rotation (1, -6), J's new coordinates would be (y + 1, -x - 6). The options listed are for point J' after rotation. Only Option 1, which is (1, -8), cannot be immediately dismissed as it aligns with the y-coordinate of the rotation point. However, without the original position of J, we cannot confirm this definitively and would require more information to provide a fully accurate answer.