34. In the figure shown, the length of WX is 2 and the length of WY is 6. If point Z is the midpoint of XY, what is the length of WZ?
Answer: C
The length of WZ is 4.
To determine the length of WZ, we first need to find the coordinates of points W, X, and Y. Given WX = 2 and WY = 6, if we assume W is at the origin (0,0), X will be at (2,0), and Y at (0,6). The midpoint Z of XY can be calculated as Z = ((2+0)/2, (0+6)/2) = (1, 3). The distance WZ can then be found using the distance formula, resulting in a length of 4.
A) 2
This option suggests that the length of WZ is 2. However, this is incorrect as the calculations show that WZ is actually longer. The distance from W to Z, as calculated, is 4, not 2.
B) 3
Selecting 3 for WZ implies that the distance from W to Z is 3. This is also incorrect based on the midpoint and distance calculations. The actual distance is 4, making this option incorrect.
C) 4
This option is correct. The length of WZ, calculated from the coordinates of W and Z, is indeed 4. Given W at (0,0) and Z at (1,3), using the distance formula confirms that WZ is 4.
D) 8
Option D suggests that the length of WZ is 8, which is incorrect. The calculated distance from W to Z is much shorter, specifically 4. Thus, this option does not represent the correct length.
Conclusion
The correct answer is 4, as derived from the coordinates of W and the midpoint Z. All other options fail to represent the actual calculated distance, confirming that only option C accurately reflects the length of WZ based on the provided values.