Question

Triangle XYZ is drawn with vertices X(1, 2), Y(2, 5), Z(3, 4). Determine the translation direction and number of units if Z′(9, 4).

6 units down
6 units up
6 units to the right
6 units to the left

Answer 1

To find the translation direction and number of units for point Z from Z(3, 4) to Z′(9, 4), we need to calculate the difference in their coordinates.

The original coordinates of point Z are (3, 4). The new coordinates of point Z′ are (9, 4).

1. **Find the change in the x-coordinate:**
\[
x' - x = 9 - 3 = 6
\]

2. **Find the change in the y-coordinate:**
\[
y' - y = 4 - 4 = 0
\]

So, the translation is:
- 6 units to the right (since the x-coordinate increased from 3 to 9).
- 0 units vertically (the y-coordinate remains the same).

Based on this analysis, the translation from Z to Z′ is 6 units to the right. Therefore, the correct option is:
**6 units to the right.**