Answered

Welcome to Westonci.ca, the ultimate question and answer platform. Get expert answers to your questions quickly and accurately. Get accurate and detailed answers to your questions from a dedicated community of experts on our Q&A platform. Join our platform to connect with experts ready to provide precise answers to your questions in different areas.

Point A is located at (1,10) and point B is located at (20,18). What point partitions the direction line segment AB inot a 2:5 ratio?

Point A Is Located At 110 And Point B Is Located At 2018 What Point Partitions The Direction Line Segment AB Inot A 25 Ratio class=

Sagot :

Given a segment joining the points A = (1, 10) and B = (20, 18).

To find the point (a, b) that partitions the segment AB into a 2:5 ratio, we use the equations:

[tex]\begin{gathered} \frac{a-1}{20-a}=\frac{2}{5}\ldots(1) \\ \frac{b-10}{18-b}=\frac{2}{5}\ldots(2) \end{gathered}[/tex]

That is, the 2:5 ratio also holds for the x and y coordinates. Solving equation (1) for a:

[tex]\begin{gathered} 5(a-1)=2(20-a) \\ 5a-5=40-2a \\ 7a=45 \\ a=\frac{45}{7}=6\frac{3}{7} \end{gathered}[/tex]

Now, solving equation (2) for b:

[tex]\begin{gathered} 5(b-10)=2(18-b) \\ 5b-50=36-2b \\ 7b=86 \\ b=\frac{86}{7}=12\frac{2}{7} \end{gathered}[/tex]

So the point is:

[tex](6\frac{3}{7},12\frac{2}{7})[/tex]

We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. We appreciate your time. Please come back anytime for the latest information and answers to your questions. Thank you for visiting Westonci.ca, your go-to source for reliable answers. Come back soon for more expert insights.