Triangle ABC has vertices of A(1, 2), B(2, 4), and C(2, 1). Which of the following describes the translation if B' has coordinates (-2, 3)?
Question
Triangle ABC has vertices of A(1, 2), B(2, 4), and C(2, 1). Which of the following describes the translation if B' has coordinates (-2, 3)?
Solution
To find the translation, we need to determine how much we moved from point B to point B'.
The coordinates of point B are (2, 4) and the coordinates of point B' are (-2, 3).
To find the horizontal translation (x-direction), subtract the x-coordinate of B from the x-coordinate of B'.
-2 (x-coordinate of B') - 2 (x-coordinate of B) = -4.
This means we moved 4 units to the left.
To find the vertical translation (y-direction), subtract the y-coordinate of B from the y-coordinate of B'.
3 (y-coordinate of B') - 4 (y-coordinate of B) = -1.
This means we moved 1 unit down.
So, the translation that moves point B to point B' is 4 units to the left and 1 unit down.
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