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End of Semester Test: Geometry, Semester A

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Select the correct answer.

The endpoints of WX are *W*(2,-7) and *X*(5,-4).

What is the length of WX?

 **A.** 

3

 **B.** 

6

 **C.** 

18

 **D.** 

6

 **E.** 

3⁢2

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To find the length of the segment \( WX \) between points \( W(2, -7) \) and \( X(5, -4) \), we can use the **distance formula**:

\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]

Here, \( W(2, -7) \) has coordinates \( (x_1, y_1) \) and \( X(5, -4) \) has coordinates \( (x_2, y_2) \). Plugging in these values:

\[
d = \sqrt{(5 - 2)^2 + (-4 + 7)^2}
\]
\[
d = \sqrt{(3)^2 + (3)^2}
\]
\[
d = \sqrt{9 + 9}
\]
\[
d = \sqrt{18}
\]
\[
d \approx 4.24
\]

The length of segment \( WX \) is approximately \( 4.24 \), which does not match the answer choices exactly. However, none of the listed choices fit this result perfectly, which suggests a potential issue in the given options.

Would you like further clarification on this, or should we proceed with additional analysis?

### Related questions:
1. What is the midpoint of segment \( WX \)?
2. How is the distance formula derived from the Pythagorean theorem?
3. What would the distance be if \( W \) and \( X \) had different coordinates?
4. Can you find the equation of the line passing through points \( W \) and \( X \)?
5. How does the distance formula change in three-dimensional space?

### Tip:
Always double-check your calculations and units when working with geometry to avoid small mistakes.

The endpoints of WX are W(2,-7) and X(5,-4). What is the length of WX?

Learn how to find the distance between points W(2,-7) and X(5,-4) using the distance formula. This geometry problem applies key concepts from coordinate geometry and the Pythagorean theorem. Suitable for students in Grades 9-10.

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