Question

1
select the correct answer from each drop - down menu.
a sequence of transformations maps ( \triangle abc ) to ( \triangle abc ). the sequence of transformations that maps ( \triangle abc ) to ( \triangle abc ) is a reflection across the

followed by a translation

Explanation:

Step1: Determine the reflection axis

By observing the \(y -\)coordinates of corresponding points (e.g., for point \(A\) and \(A'\), \(B\) and \(B'\), \(C\) and \(C'\)), we can see that the \(y -\)coordinates change their signs. For a point \((x,y)\) reflected across the \(x -\)axis, the new point is \((x, - y)\). So, the first transformation is a reflection across the \(x -\)axis.

Step2: Calculate the translation distance

For the \(x -\)coordinate of a point (take point \(C\) with \(x = - 4\) and \(C'\) with \(x = 14\)), the translation distance \(d\) is calculated as \(d=14-(-4)=18\). So, the second transformation is a translation \(18\) units to the right.

Answer:

1. \(x -\)axis
2. \(18\) units to the right