Question

the graph shows pentagons vwxyz and vwxyz. which of the following transformations maps vwxyz onto vwxyz? translation up 4 units translation up 7 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 translation

Translation up by a certain number of units changes the y - coordinates. For translation up 4 units, if a point $(x,y)$ in VWXYZ is translated, the new point is $(x,y + 4)$. For translation up 7 units, the new point is $(x,y+7)$. By observing the graph, we can see that the shape is not just translated up.

Step2: Analyze reflection

For reflection across the x - axis, the rule is $(x,y)\to(x, - y)$. For reflection across the y - axis, the rule is $(x,y)\to(-x,y)$. By observing the orientation of the pentagons, it is not a reflection across the x - axis or y - axis.

Step3: Analyze rotation

For a 90° clockwise rotation around the origin, the rule is $(x,y)\to(y,-x)$. For a 90° counter - clockwise rotation around the origin, the rule is $(x,y)\to(-y,x)$. For a 180° rotation around the origin, the rule is $(x,y)\to(-x,-y)$. By observing the orientation and position of the pentagons, we can see that a 180° rotation around the origin maps VWXYZ onto V'W'X'Y'Z'.

Answer:

rotation 180° around the origin