Question

quadrilateral k r w b is shown on the coordinate grid. apply the sequence of transformations below to quadrilateral k r w b.
step 1: (x, y) → (x + 4, y - 3)
step 2: (x, y) → (-x, -y)
what are the coordinates of b?

Explanation:

Step1: Find coordinates of \( B \)

From the graph, the coordinates of \( B \) are \( (2,6) \).

Step2: Apply the first transformation \((x,y)\to(x + 4,y-3)\)

For \( B(2,6) \), substitute \( x = 2 \) and \( y = 6 \) into \( (x + 4,y-3) \).
\( x+4=2 + 4=6 \), \( y - 3=6-3 = 3 \). So \( B'=(6,3) \).

Step3: Apply the second transformation \((x,y)\to(-x,-y)\)

For \( B'(6,3) \), substitute \( x = 6 \) and \( y = 3 \) into \( (-x,-y) \).
\( -x=-6 \), \( -y=-3 \). So \( B''=(-6,-3) \).

Answer:

\( B'=(6,3) \), \( B''=(-6,-3) \)