Question

find the composition of transformations that maps \\( \triangle a b c \\) to \\( \triangle a ^ { prime } b ^ { prime } c ^ { prime } \\).
reflect over the \\( y - \\) axis, then translate \\( ( x + 1, y + ? ) \\).

Explanation:

Step1: Find coordinates of \( B \)

The coordinates of \( B \) are \( (-3,4) \).

Step2: Reflect \( B \) over \( y - axis \)

When reflecting a point \( (x,y) \) over the \( y - axis \), the rule is \( (x,y)\to(-x,y) \). So, \( (-3,4)\to(3,4) \).

Step3: Find the translation for \( y - coordinate \)

The \( y - coordinate \) of \( B' \) is \( 0 \). Let the translation for \( y - coordinate \) be \( k \). Using the formula \( y + k \), we have \( 4 + k=0 \). Solving for \( k \), we get \( k=- 4 \).

Answer:

\(-4\)