Final answer:
To translate vertex Y of triangle XYZ according to the given coordinates, each vertex of the triangle must be moved 8 units to the left and 6 units up.
Step-by-step explanation:
The question is asking about the translation of a geometric figure on a coordinate plane. To identify the correct steps for translating vertex Y of triangle XYZ, we need to compare the initial and final coordinates of this vertex. The initial coordinates are (6, −4) and the final coordinates are (−2, 2). By comparing these, we can find the change in the x and y positions, which are the displacement components.
To find the horizontal displacement, we subtract the x-coordinate of the final position from the x-coordinate of the initial position: −2 − 6 = −8. This indicates a translation of 8 units to the left, as motion to the left is negative. For the vertical displacement, we subtract the y-coordinate of the initial position from the y-coordinate of the final position: 2 - (−4) = 6. This indicates a translation of 6 units upward, as motion upward is positive. Thus, each vertex of the triangle needs to be moved 8 units to the left and 6 units up.
Answer: A. Move each vertex 8 units to the left and 6 units up.