Question

describe the transformation which maps the pre-image to the image.
graph of two triangles (pre - image below x - axis, image above x - axis) with vertices labeled l, j, k (pre - image) and l, j, k (image)
options:

• translation 2 units down
• reflection across x - axis
• reflection across y - axis
• translation 4 units down

Explanation:

To determine the transformation, we analyze the coordinates of corresponding points (e.g., \( L \) and \( L' \), \( J \) and \( J' \), \( K \) and \( K' \)) in the pre - image (lower triangle) and the image (upper triangle). A reflection across the \( x \) - axis changes the sign of the \( y \) - coordinate of a point \((x,y)\) to \((x, - y)\). Looking at the graph, the pre - image points and image points seem to have their \( y \) - coordinates negated, which is characteristic of a reflection across the \( x \) - axis. A translation down would shift all points vertically without changing the sign of the \( y \) - coordinate, and a reflection across the \( y \) - axis would change the sign of the \( x \) - coordinate, which is not the case here. Also, the vertical distance between corresponding points is 4 units, but the nature of the transformation (sign change of \( y \) - coordinate) indicates reflection across \( x \) - axis rather than a translation of 4 units down (translation would not flip the triangle over the \( x \) - axis).

Answer:

Reflection across x - axis