Triangle XYZ is drawn with vertices X(1, 2), Y(2, 5), Z(3, 4). Determine the translation direction and number of units if Y′(2, −2).

Question

7 units down
7 units up
7 units to the right
7 units to the left

Answer 1

To determine the translation direction and number of units that point Y(2, 5) moves to Y′(2, −2), we need to examine the change in the y-coordinate, as the x-coordinate remains the same.

The original point Y is located at (2, 5) and the translated point Y′ is located at (2, −2).

1. Calculate the change in the y-coordinate: \[ \text{Change in y} = y' - y = -2 - 5 = -7 \]

The negative sign indicates that the point is moved down vertically. Since the x-coordinate remains unchanged, the movement is only in the vertical direction.

2. Conclusion: Since the y-coordinate decreases by 7 units, we conclude that the translation is 7 units down.

Answer: 7 units down