1. Triangles KLM and MNO are simdar rightr triangles. KM is equal to the slope of MO, Which proportion can be used to show that the slope of A. -3-9 -6-(-3) 2-(-6) 4-2 в. -3-2 -6-4 9-(-6) -3-2 2-(-6) 4-2 -3-9 -6-(-3) D. -2-(-3) 4-(-6) %3D -6-9 2-(-3)
1. Triangles KLM and MNO are simdar rightr triangles. KM is equal to the slope of MO, Which proportion can be used to show that the slope of A. -3-9 -6-(-3) 2-(-6) 4-2 в. -3-2 -6-4 9-(-6) -3-2 2-(-6) 4-2 -3-9 -6-(-3) D. -2-(-3) 4-(-6) %3D -6-9 2-(-3)
Algebra and Trigonometry (6th Edition)
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ChapterP: Prerequisites: Fundamental Concepts Of Algebra
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Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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The graph shows two right triangles on a coordinate plane. Triangle \( KLM \) is larger and located in the second quadrant, while triangle \( MNO \) is smaller and located in the fourth quadrant. Both triangles share the line segment \( KM \).
Points are labeled as follows:
- \( K \) is at the upper left.
- \( L \) is directly below \( K \).
- \( M \) is on the line shared by both triangles.
- \( N \) is directly to the right of \( M \).
- \( O \) is further right from \( N \).
2. **Question:**
Which proportion can be used to show that the slope of \( KM \) is equal to the slope of \( MO \)?
**Options:**
A.
\[
\frac{-3 - 9}{2 - (-6)} = \frac{-6 - (-3)}{4 - 2}
\]
B.
\[
\frac{-3 - 2}{9 - (-6)} = \frac{-6 - 4}{-3 - 2}
\]
C.
\[
\frac{2 - (-6)}{-3 - 9} = \frac{4 - 2}{-6 - (-3)}
\]
D.
\[
\frac{-2 - (-3)}{-6 - 9} = \frac{4 - (-6)}{2 - (-3)}
\]
**Solution Explanation:**
1. **Identify Points Coordinates:**
- Determine the coordinates of points \( K \), \( L \), \( M \), \( N \), and \( O \) from the graph.
2. **Calculate Slopes:**
- Use the slope formula \( \frac{y_2 - y_1}{x_2 - x_1} \) to calculate the slope of \( KM \) and \( MO \).
3. **Verify Proportions:**
- Check which proportion correctly represents the equality of the slopes calculated.
**Note:**
This task challenges learners to apply their understanding](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F11fd6488-16bc-4d02-9ace-22093960af50%2F4cc7f4ab-8dd4-4a16-a822-5a47b09f4679%2Fhsyawa8_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem:**
1. **Triangles \( \triangle KLM \) and \( \triangle MNO \) are similar right triangles.**
The graph shows two right triangles on a coordinate plane. Triangle \( KLM \) is larger and located in the second quadrant, while triangle \( MNO \) is smaller and located in the fourth quadrant. Both triangles share the line segment \( KM \).
Points are labeled as follows:
- \( K \) is at the upper left.
- \( L \) is directly below \( K \).
- \( M \) is on the line shared by both triangles.
- \( N \) is directly to the right of \( M \).
- \( O \) is further right from \( N \).
2. **Question:**
Which proportion can be used to show that the slope of \( KM \) is equal to the slope of \( MO \)?
**Options:**
A.
\[
\frac{-3 - 9}{2 - (-6)} = \frac{-6 - (-3)}{4 - 2}
\]
B.
\[
\frac{-3 - 2}{9 - (-6)} = \frac{-6 - 4}{-3 - 2}
\]
C.
\[
\frac{2 - (-6)}{-3 - 9} = \frac{4 - 2}{-6 - (-3)}
\]
D.
\[
\frac{-2 - (-3)}{-6 - 9} = \frac{4 - (-6)}{2 - (-3)}
\]
**Solution Explanation:**
1. **Identify Points Coordinates:**
- Determine the coordinates of points \( K \), \( L \), \( M \), \( N \), and \( O \) from the graph.
2. **Calculate Slopes:**
- Use the slope formula \( \frac{y_2 - y_1}{x_2 - x_1} \) to calculate the slope of \( KM \) and \( MO \).
3. **Verify Proportions:**
- Check which proportion correctly represents the equality of the slopes calculated.
**Note:**
This task challenges learners to apply their understanding
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