Question

identify the following composition transformation mapping: (x,y)→(−x,−y + 5)
option #1: rotate 180 degrees, then down 5
option #2: reflect across the x - axis, then up 5
option #3: reflect across the y - axis, then up 5
option #4: rotate 180 degrees, then up 5
(1 point)

Explanation:

Step1: Analyze x - coordinate change

The change from \(x\) to \(-x\) can be achieved by a 180 - degree rotation or a reflection across the y - axis. A 180 - degree rotation about the origin changes \((x,y)\) to \((-x,-y)\) and a reflection across the y - axis also changes \(x\) to \(-x\).

Step2: Analyze y - coordinate change

The change from \(y\) to \(-y + 5\). First, changing \(y\) to \(-y\) can be a 180 - degree rotation or a reflection across the x - axis. Then adding 5 to \(-y\) means moving the point up 5 units. A 180 - degree rotation about the origin changes \((x,y)\) to \((-x,-y)\) and then adding 5 to the y - coordinate moves the point up 5 units.

Answer:

Option #4: rotate 180 degrees, then up 5