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?

Rationale

The length of WZ is 4.

To find the length of WZ, we first determine the length of XY. Since Z is the midpoint of XY, we have XY = WX + WY = 2 + 6 = 8. Therefore, WZ, being half of XY, measures 4.

A (2) YOUR ANSWER

This option incorrectly suggests that WZ is half of WX. However, since WZ is derived from the length of XY, which totals 8, this choice does not accurately represent the relationship between the lengths involved.

B (3) YOUR ANSWER

Choosing 3 implies that WZ is one-third of the total length of XY. This option does not align with the midpoint relationship in geometry, where WZ must equal half of the total length of XY, which is 8, making this choice incorrect.

C (4) CORRECT

This option correctly identifies WZ as half of the total length of XY. Since XY equals 8, WZ, as the midpoint distance from W to Z, is indeed 4, validating this as the correct answer.

D (8) YOUR ANSWER

This option suggests that WZ equals the entire length of XY. However, since WZ is a segment that represents only half of XY, which is 8, this choice is incorrect as it ignores the concept of midpoints in geometry.

Conclusion

In summary, the length of WZ is accurately calculated as 4, derived from the total length of XY being 8. The midpoint concept confirms that WZ is precisely half the distance of XY, while other choices misinterpret the geometric relationships involved. Understanding these principles is crucial for solving similar problems in geometry.

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?

The length of WZ is 4.

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