Answered

Westonci.ca is your trusted source for finding answers to a wide range of questions, backed by a knowledgeable community. Discover reliable solutions to your questions from a wide network of experts on our comprehensive Q&A platform. Discover detailed answers to your questions from a wide network of experts on our comprehensive Q&A platform.

What are the coordinates of the point on the directed line segment from (1, -5)(1,−5) to (10, 1)(10,1) that partitions the segment into a ratio of 1 to 5?

Sagot :

Check the picture below.

[tex]\textit{internal division of a line segment using ratios} \\\\\\ A(1,-5)\qquad B(10,1)\qquad \qquad \stackrel{\textit{ratio from A to B}}{1:5} \\\\\\ \cfrac{A\underline{C}}{\underline{C} B} = \cfrac{1}{5}\implies \cfrac{A}{B} = \cfrac{1}{5}\implies 5A=1B\implies 5(1,-5)=1(10,1)[/tex]

[tex](\stackrel{x}{5}~~,~~ \stackrel{y}{-25})=(\stackrel{x}{10}~~,~~ \stackrel{y}{1})\implies C=\underset{\textit{sum of the ratios}}{\left( \cfrac{\stackrel{\textit{sum of x's}}{5+10}}{1+5}~~,~~\cfrac{\stackrel{\textit{sum of y's}}{-25+1}}{1+5} \right)} \\\\\\ C=\left( \cfrac{15}{6}~~,~~\cfrac{-24}{6} \right)\implies C=\left(\cfrac{5}{2}~~,~~-4 \right)[/tex]

View image jdoe0001
Thanks for stopping by. We are committed to providing the best answers for all your questions. See you again soon. Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. Thank you for visiting Westonci.ca. Stay informed by coming back for more detailed answers.