Question

the graph shows squares fghi and fghi. which of the following transformations maps fghi onto fghi? translation right 6 units and up 12 units; translation right 12 units and up 6 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:

Step1: Identify coordinates of a point

Take point \( F \) in square \( FGHI \). From the graph, \( F \) has coordinates \( (1, -8) \) (assuming the grid, let's confirm: looking at the lower square, \( F \) is at \( x = 1 \), \( y = -8 \)). Point \( F' \) in \( F'G'H'I' \) has coordinates \( (7, 4) \).

Step2: Calculate horizontal and vertical shifts

Horizontal shift: \( 7 - 1 = 6 \) (right 6 units). Vertical shift: \( 4 - (-8) = 12 \) (up 12 units). Let's check another point, say \( H \). \( H \) is \( (0, -5) \), \( H' \) is \( (6, 7) \). Horizontal: \( 6 - 0 = 6 \), Vertical: \( 7 - (-5) = 12 \). This matches the first transformation.

Answer:

translation right 6 units and up 12 units