Question

10 triangle qrs is transformed using the rule $(-x,y + 2)$ to create triangle $qrs$.
(a)
what are the x - and y - coordinates of $r$?
enter your answer in the boxes provided.
$r$(
)
(b) is $\triangle qrs\cong\triangle qrs$? justify your reasoning using the definition of congruence in terms of rigid motions.

Explanation:

Step1: Find the coordinates of \( R \)

From the graph, the coordinates of \( R \) are \( (-3,1) \).

Step2: Apply the transformation rule \( (-x,y + 2) \)

For the \( x \)-coordinate: \( -(-3)=3 \).
For the \( y \)-coordinate: \( 1+2 = 3 \).

for part (b):

Step1: Analyze the transformation

The transformation \( (-x,y + 2) \) is a combination of a reflection over the \( y \)-axis (because of the \( -x \) part) and a translation up by \( 2 \) units (because of the \( y+2 \) part).

Step2: Recall the properties of rigid motions

Rigid motions (reflections, translations, rotations) preserve side - lengths and angle measures.
Since \( \triangle QRS \) is transformed using rigid motions (reflection and translation) to get \( \triangle Q'R'S' \), all corresponding sides and angles of \( \triangle QRS \) and \( \triangle Q'R'S' \) are equal.

Answer:

\( R'(3,3) \)