Question

transformations test (topic 4)
a translation is used to map ( a(-5, 13) ) to ( a(2, 9) ). if the same translation is used to map ( b(4, -2) ), then its image, ( b ), would have coordinates of
( circ b(8, -5) )
( circ b(-3, 2) )
( circ b(11, -6) )
( circ b(7, -4) )

Explanation:

Step1: Find the translation vector

To find the translation vector, we calculate the difference between the coordinates of \( A' \) and \( A \). For the \( x \)-coordinate: \( 2 - (-5) = 7 \). For the \( y \)-coordinate: \( 9 - 13 = -4 \). So the translation vector is \( (7, -4) \).

Step2: Apply the translation to point \( B \)

We add the translation vector to the coordinates of \( B(4, -2) \). For the \( x \)-coordinate: \( 4 + 7 = 11 \). For the \( y \)-coordinate: \( -2 + (-4) = -6 \). So the coordinates of \( B' \) are \( (11, -6) \).

Answer:

\( B'(11, -6) \)