Question

the graph shows pentagons ijklm and ijklm.
which of the following transformations maps ijklm onto ijklm?
options:

• translation down 10 units
• translation down 4 units
• reflection across the x - axis
• reflection across the y - axis
• rotation 90° clockwise around the origin
• rotation 90° counterclockwise around the origin
• rotation 180° around the origin

Explanation:

To determine the transformation mapping \( IJKLM \) to \( I'J'K'L'M' \), we analyze the coordinates of corresponding vertices (e.g., \( J(0,5) \) and \( J'(0,-5) \), \( K(3,5) \) and \( K'(3,-5) \), etc.). A reflection across the \( x \)-axis changes the sign of the \( y \)-coordinate (\( (x,y) \to (x,-y) \)), which matches the relationship between the original and transformed vertices. Translations would shift all points by a fixed amount, but here the \( x \)-coordinates remain the same while \( y \)-coordinates are negated. Rotations would change \( x \)- and \( y \)-coordinates in a rotational pattern, which is not observed here. Thus, reflection across the \( x \)-axis is the correct transformation.

Answer:

reflection across the x - axis