Question

check for understanding (eoc prep)
triangle xyz is transformed to create triangle ( xyz ) using the rule ( (x,y)\to(x + b,y + c) ).

• triangle xyz has the vertices ( (3,-2),(3,-4) ), and ( (0,-4) ), respectively.
• triangle ( xyz ) has the vertices ( (-1,5),(-1,3) ), and ( (-4,3) ), respectively.

what are the values of ( b ) and ( c )?
( b=)( c= )

Explanation:

Step1: Calculate the value of \( b \)

Take one pair of corresponding vertices, say \( (3,-2) \) and \( (-1,5) \). For the \( x \)-coordinate, using the rule \( x\to x + b \).
If \( x = 3 \) and \( x'=-1 \), then \( 3 + b=-1 \).
Solve for \( b \): \( b=-1 - 3=-4 \).

Step2: Calculate the value of \( c \)

Using the same pair of vertices \( (3,-2) \) and \( (-1,5) \). For the \( y \)-coordinate, using the rule \( y\to y + c \).
If \( y=-2 \) and \( y' = 5 \), then \( -2 + c=5 \).
Solve for \( c \): \( c=5+ 2 = 7 \).

Answer:

\( b=-4 \), \( c = 7 \)