Welcome to Westonci.ca, the place where your questions find answers from a community of knowledgeable experts. Explore a wealth of knowledge from professionals across various disciplines on our comprehensive Q&A platform. Join our Q&A platform to connect with experts dedicated to providing accurate answers to your questions in various fields.
Sagot :
The student's answer is actually incorrect. Let's analyze the student's work step-by-step and identify the correct approach.
1. Total Sections Calculation:
To partition the directed line segment from [tex]\( A \)[/tex] to [tex]\( B \)[/tex] in a ratio of [tex]\( 3:4 \)[/tex], we first need to determine the total number of sections:
[tex]\[ \text{total sections} = 3 + 4 = 7 \][/tex]
2. Fraction for the Partition:
We then use the fraction that corresponds to the given ratio. Since we want the point [tex]\( C \)[/tex] such that it partitions the segment [tex]\( AB \)[/tex] in the ratio [tex]\( 3:4 \)[/tex]:
[tex]\[ \text{fraction} = \frac{3}{7} \][/tex]
3. Calculate the Coordinate of Point [tex]\( C \)[/tex]:
The formula to find the coordinate of point [tex]\( C \)[/tex] is given by:
[tex]\[ C = \left( \frac{3}{7} \right)(B - A) + A \][/tex]
Plugging in the given values [tex]\( A = -6 \)[/tex] and [tex]\( B = 2 \)[/tex]:
[tex]\[ C = \left( \frac{3}{7} \right)(2 - (-6)) + (-6) \][/tex]
[tex]\[ C = \left( \frac{3}{7} \right)(8) + (-6) \][/tex]
[tex]\[ C = \left( \frac{24}{7} \right) - 6 \][/tex]
[tex]\[ C = 3.4285714285714284 - 6 \][/tex]
[tex]\[ C = -2.5714285714285716 \][/tex]
4. Verification:
The correct position of point [tex]\( C \)[/tex] is approximately [tex]\(-2.57\)[/tex], not 0.
Thus, the student's error lies in the initial application of the ratio. They mistakenly used the fraction [tex]\( \frac{3}{4} \)[/tex] of the length instead of the correct fraction [tex]\( \frac{3}{7} \)[/tex].
So, the correct answer to your question is:
No, the student should have added [tex]\(3 + 4\)[/tex] to get the total number of sections, and used the fraction [tex]\( \frac{3}{7} \)[/tex] instead of [tex]\( \frac{3}{4} \)[/tex].
1. Total Sections Calculation:
To partition the directed line segment from [tex]\( A \)[/tex] to [tex]\( B \)[/tex] in a ratio of [tex]\( 3:4 \)[/tex], we first need to determine the total number of sections:
[tex]\[ \text{total sections} = 3 + 4 = 7 \][/tex]
2. Fraction for the Partition:
We then use the fraction that corresponds to the given ratio. Since we want the point [tex]\( C \)[/tex] such that it partitions the segment [tex]\( AB \)[/tex] in the ratio [tex]\( 3:4 \)[/tex]:
[tex]\[ \text{fraction} = \frac{3}{7} \][/tex]
3. Calculate the Coordinate of Point [tex]\( C \)[/tex]:
The formula to find the coordinate of point [tex]\( C \)[/tex] is given by:
[tex]\[ C = \left( \frac{3}{7} \right)(B - A) + A \][/tex]
Plugging in the given values [tex]\( A = -6 \)[/tex] and [tex]\( B = 2 \)[/tex]:
[tex]\[ C = \left( \frac{3}{7} \right)(2 - (-6)) + (-6) \][/tex]
[tex]\[ C = \left( \frac{3}{7} \right)(8) + (-6) \][/tex]
[tex]\[ C = \left( \frac{24}{7} \right) - 6 \][/tex]
[tex]\[ C = 3.4285714285714284 - 6 \][/tex]
[tex]\[ C = -2.5714285714285716 \][/tex]
4. Verification:
The correct position of point [tex]\( C \)[/tex] is approximately [tex]\(-2.57\)[/tex], not 0.
Thus, the student's error lies in the initial application of the ratio. They mistakenly used the fraction [tex]\( \frac{3}{4} \)[/tex] of the length instead of the correct fraction [tex]\( \frac{3}{7} \)[/tex].
So, the correct answer to your question is:
No, the student should have added [tex]\(3 + 4\)[/tex] to get the total number of sections, and used the fraction [tex]\( \frac{3}{7} \)[/tex] instead of [tex]\( \frac{3}{4} \)[/tex].
We hope our answers were helpful. Return anytime for more information and answers to any other questions you may have. Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. Westonci.ca is committed to providing accurate answers. Come back soon for more trustworthy information.