Question

find a congruence transformation that maps (\triangle rst) to (\triangle uvw).

Explanation:

Step1: Analyze transformation for problem 2

First, observe the position of \(\triangle RST\) and \(\triangle UVW\). Notice that \(\triangle RST\) can be reflected over the \(x -\)axis. Let's check the \(y -\)coordinates. For a point \((x,y)\) reflected over the \(x -\)axis, the transformation rule is \((x,y)\to(x, - y)\). After reflection over the \(x -\)axis, \(\triangle RST\) and \(\triangle UVW\) have the same orientation in terms of left - right and front - back (in 2D sense).

Step2: Analyze transformation for problem 3

Look at the position of \(\triangle RST\) and \(\triangle UVW\). We can first translate \(\triangle RST\). Count the number of units. Translate \(\triangle RST\) 6 units up. The translation rule for a point \((x,y)\) is \((x,y)\to(x,y + 6)\). After translation, check the orientation. Then, notice that we can also consider a rotation. But if we just focus on translation (since congruence transformations include translation, rotation, reflection), a translation of 6 units up maps \(\triangle RST\) to \(\triangle UVW\) (by checking the vertical distance between corresponding vertices).

Answer:

For problem 2: A reflection over the \(x -\)axis maps \(\triangle RST\) to \(\triangle UVW\).
For problem 3: A translation of 6 units up maps \(\triangle RST\) to \(\triangle UVW\).