Explore Westonci.ca, the top Q&A platform where your questions are answered by professionals and enthusiasts alike. Connect with a community of experts ready to provide precise solutions to your questions quickly and accurately. Get precise and detailed answers to your questions from a knowledgeable community of experts on our Q&A platform.
Sagot :
To find the coordinates of point [tex]\( P \)[/tex] that partitions the line segment [tex]\( AB \)[/tex] into a part-to-whole ratio of [tex]\( 1:5 \)[/tex], we first need to understand what this ratio represents and how to use it in our calculations.
Given:
- Line segment [tex]\( AB \)[/tex] with endpoints at [tex]\( A(-9, 3) \)[/tex] and [tex]\( B(1, 8) \)[/tex].
- Part-to-whole ratio [tex]\( 1 : 5 \)[/tex].
In order to determine the correct placement of point [tex]\( P \)[/tex] along segment [tex]\( AB \)[/tex], we need to convert this part-to-whole ratio into a fraction.
The ratio [tex]\( 1 : 5 \)[/tex] means that if we were to divide the segment into a total of 6 equal parts (since [tex]\( 1 + 5 = 6 \)[/tex]), point [tex]\( P \)[/tex] would be placed after the first part when moving from [tex]\( A \)[/tex] to [tex]\( B \)[/tex].
This translates to the fraction of the distance from [tex]\( A \)[/tex] to [tex]\( P \)[/tex] relative to the entire segment [tex]\( AB \)[/tex]. The fraction is:
[tex]\[ \frac{m}{m+n} = \frac{1}{1+5} = \frac{1}{6} \][/tex]
Therefore, the fraction [tex]\(\frac{m}{m+n} \)[/tex] equals [tex]\( \frac{1}{6} \)[/tex].
Given:
- Line segment [tex]\( AB \)[/tex] with endpoints at [tex]\( A(-9, 3) \)[/tex] and [tex]\( B(1, 8) \)[/tex].
- Part-to-whole ratio [tex]\( 1 : 5 \)[/tex].
In order to determine the correct placement of point [tex]\( P \)[/tex] along segment [tex]\( AB \)[/tex], we need to convert this part-to-whole ratio into a fraction.
The ratio [tex]\( 1 : 5 \)[/tex] means that if we were to divide the segment into a total of 6 equal parts (since [tex]\( 1 + 5 = 6 \)[/tex]), point [tex]\( P \)[/tex] would be placed after the first part when moving from [tex]\( A \)[/tex] to [tex]\( B \)[/tex].
This translates to the fraction of the distance from [tex]\( A \)[/tex] to [tex]\( P \)[/tex] relative to the entire segment [tex]\( AB \)[/tex]. The fraction is:
[tex]\[ \frac{m}{m+n} = \frac{1}{1+5} = \frac{1}{6} \][/tex]
Therefore, the fraction [tex]\(\frac{m}{m+n} \)[/tex] equals [tex]\( \frac{1}{6} \)[/tex].
We hope our answers were useful. Return anytime for more information and answers to any other questions you have. Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. We're glad you chose Westonci.ca. Revisit us for updated answers from our knowledgeable team.