Question

△BCD ​is translated to become △B′C′D′ ​. △BCD has coordinates B(4, 2) , C(6, 2) , and D(6, 5) . ​ △B′C′D′ has coordinates B′(2, 1) , C′(4, 1) , and D′(4, 4) . Which answer describes the translation?​ vertical translation of 2 followed by a horizontal translation of 1 horizontal translation of ​ −2 ​followed by a vertical translation of −1 vertical translation of 1 followed by a horizontal translation of 2 horizontal translation of ​ −1 ​​​followed by a vertical translation of ​ −2 ​

Answer 1

You have to notice the pattern of the coordinates. Let's start by comparing points B and B'. The x-coordinate changes from 4 to 2, while the y-coordinate changes from 2 to 1. From this, we can say that the point moves two units to the left and 1 unit down. The same pattern is observed for the rest of the points. Thus, it means that the translation is -2 horizontally and -1 vertically.

Answer 2

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.