Question

ABC is translated onto A’B’C’. The coordinates of point A are (3, 7) and the coordinates of

point A’ are (1, 12). If the coordinates of point B are (7, 2), what are the coordinates of point
B’?
The horizontal shift from point A to point A’ is _______. The vertical shift from point A to
point A’ is _______. Since in a translation all points shift the same distance, the coordinates of
point B’ are ( ____, ____ ).

Answer 1

Answers and Step-by-step explanations:

1. The horizontal shift from point A to point A' will simply be the difference in the x-coordinates. The x-coordinate of A is 3 and the x-coordinate of A' is 1. So, we take 1 - 3 = -2. The horizontal shift is 2 units to the left.

2. The vertical shift is the difference in the y-coordinates. The y-coordinate of A is 7 and the y-coordinate of A' is 12. So, we take 12 - 7 = 5. The vertical shift is 5 units up.

3. Basically, we want to move the coordinates of B 2 units to the left and 5 units up. B is currently (7, 2). When we move 2 units to the left, we subtract 2 from the x-coordinate 7, and when we move 5 units up, we add 5 to the y-coordinate 2: B' = (7 - 2, 2 + 5) = (5, 7)

Hope this helps!

Answer 2

The horizontal shift from point A to point A’ is -2. The vertical shift from point A to point A’ is 5. Since in a translation all points shift the same distance, the coordinates of point B’ are (5, 7 ).

Explanation:

A moved two units to the left.

1 - 3 = -2

A also moved 5 units up.

12 - 7 = 5

The translation rule is:
`(x,y) -> (x - 2, y + 5)`

Apply the translation rule to point B.

`(7 -2, 2+5) = (5,7)`

B' should be (5,7).