Answer: The correct option is
(B) horizontal translation of −2 followed by a vertical translation of −1.
Step-by-step explanation: Given that triangle BCD is translated to become triangle B'C'D'. The co-ordinates of the vertices of triangle BCD are B(4, 2) , C(6, 2) , and D(6, 5) and that of triangle B′C′D′ are B′(2, 1) , C′(4, 1) , and D′(4, 4).
We are to find the correct translation.
We see the following pattern of the translation :
B(4, 2) ⇒ B'(2, 1) = (4-2, 2-1)
C(6, 2) ⇒ C'(4, 1) = (6-2, 2-1)
and
D(6, 5) ⇒ D'(4, 4) = (6-2, 5-1).
So, if (x, y) is a vertex of triangle BCD, then the corresponding vertex of triangle B'C'D' is (x-2, y-1).
Therefore, there is a horizontal translation of -2 followed by a vertical translation of -1.
Thus, option (B) is CORRECT.