**Geometry Segment Addition Postulate – Activity 1.4.1**---**Problem 6: Segment Addition Postulate****Given:**Point $ V $ is somewhere on $\overline{UW}$. If $ UV = 2x - 13 $, $ VW = -18 + 2x $, and $ UW = 17 $, then find the length of $\overline{UV}$.**Diagram:**```U ---------------------- V ---------------------- W | UV = 2x - 13 | VW = -18 + 2x | |------------------------------------------| UW = 17```**Solution Steps:**1. Apply the Segment Addition Postulate which states: \[ UV + VW = UW \] 2. Substitute the given expressions into this equation: \[ (2x - 13) + (-18 + 2x) = 17 \]3. Simplify the equation: \[ 2x - 13 - 18 + 2x = 17 \] \[ 4x - 31 = 17 \]4. Solve for $ x $: \[ 4x - 31 = 17 \] \[ 4x = 48 \] \[ x = 12 \]5. Find the length of $\overline{UV}$ by substituting $ x = 12 $ back into $ UV = 2x - 13 $: \[ UV = 2(12) - 13 \] \[ UV = 24 - 13 \] \[ UV = 11 \]**Answer:**- The length of $\overline{UV}$ is $ 11 $.**Multiple-choice options:**- $ \circ $ 12- $ \circ $ 6- $ \circ $ 11The correct answer is 11.**Contributors:**- Rayce Dendel, Academic Coach- Dave Whitehead, TeacherThis content is designed for educational purposes to enhance your understanding of the Segment Addition Postulate in geometry. ---By practicing these steps, students will

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Answered: 6. Point V is somewhere on UW. If UV =…

6. Point V is somewhere on UW. If UV = 2x-13, VW = -18+2x, and UW = 17 then find the length of UV. 2х - 13 -18 + 2x U • V 17

Elementary Geometry For College Students, 7e

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Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

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Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.

Question

**Geometry Segment Addition Postulate – Activity 1.4.1**

---

**Problem 6: Segment Addition Postulate**

**Given:**
Point $ V $ is somewhere on $\overline{UW}$. If $ UV = 2x - 13 $, $ VW = -18 + 2x $, and $ UW = 17 $, then find the length of $\overline{UV}$.

**Diagram:**
```
U ---------------------- V ---------------------- W
| UV = 2x - 13 | VW = -18 + 2x |
|------------------------------------------|
UW = 17
```

**Solution Steps:**

1. Apply the Segment Addition Postulate which states:
\[
UV + VW = UW
\]

2. Substitute the given expressions into this equation:
\[
(2x - 13) + (-18 + 2x) = 17
\]

3. Simplify the equation:
\[
2x - 13 - 18 + 2x = 17
\]
\[
4x - 31 = 17
\]

4. Solve for $ x $:
\[
4x - 31 = 17
\]
\[
4x = 48
\]
\[
x = 12
\]

5. Find the length of $\overline{UV}$ by substituting $ x = 12 $ back into $ UV = 2x - 13 $:
\[
UV = 2(12) - 13
\]
\[
UV = 24 - 13
\]
\[
UV = 11
\]

**Answer:**
- The length of $\overline{UV}$ is $ 11 $.

**Multiple-choice options:**
- $ \circ $ 12
- $ \circ $ 6
- $ \circ $ 11

The correct answer is 11.

**Contributors:**
- Rayce Dendel, Academic Coach
- Dave Whitehead, Teacher

This content is designed for educational purposes to enhance your understanding of the Segment Addition Postulate in geometry.

---

By practicing these steps, students will

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