Question

which of the following transformations maps efg onto efg? translation right 16 units translation right 18 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: Analyze x - coordinate change

The x - coordinate of a point in EFG and its corresponding point in E'F'G' changes. For example, if we consider a vertex of EFG and its image in E'F'G', the horizontal displacement is observed. Count the number of units between a point in EFG and its corresponding point in E'F'G' along the x - axis.
Let's assume a vertex of EFG has an x - coordinate \(x_1\) and its image in E'F'G' has an x - coordinate \(x_2\). By counting the grid - squares, we find that \(x_2−x_1 = 16\).

Step2: Check other transformation properties

A reflection across the x - axis would change the sign of the y - coordinate. A reflection across the y - axis would change the sign of the x - coordinate. A rotation of 90° clockwise around the origin would transform a point \((x,y)\) to \((y, - x)\), a 90° counter - clockwise rotation would transform \((x,y)\) to \((-y,x)\) and a 180° rotation would transform \((x,y)\) to \((-x,-y)\). None of these rotation or reflection rules match the transformation from EFG to E'F'G'.

Answer:

translation right 16 units