Discover the best answers at Westonci.ca, where experts share their insights and knowledge with you. Experience the convenience of finding accurate answers to your questions from knowledgeable experts on our platform. Discover in-depth answers to your questions from a wide network of professionals on our user-friendly Q&A platform.
Sagot :
Given:
The point (4, 2) divides the line joining the points (2, -4) and (8, 14).
To find: The ratio
​Explanation:
Let the ratio be,
[tex]m:n=k:1[/tex]Using the section formula,
[tex]P=\lparen\frac{mx_2+nx_{1,}}{m+n},\frac{my_2+ny_1}{m+n})[/tex]Here, we have
[tex]\begin{gathered} m=k,n=1 \\ x_1=2,y_1=-4 \\ x_2=8,y_2=14 \end{gathered}[/tex]On substitution we get,
[tex](4,2)=\lparen\frac{8k+2}{k+1},\frac{14k+4}{k+1})[/tex]Equating the coordinates we get,
[tex]\begin{gathered} 4=\frac{8k+2}{k+1} \\ 4\left(k+1\right)=8k+2 \\ 4k+4=8k+2 \\ 4k=2 \\ k=\frac{1}{2} \end{gathered}[/tex]Since,
[tex]\begin{gathered} k=\frac{1}{2} \\ \therefore m:n=\frac{1}{2}:1 \\ m:n=1:2 \end{gathered}[/tex]Hence, the ratio in which the point (4, 2) divides the line joining the points (2, -4) and (8, 14) is 1: 2.
Final answer: The ratio is,
[tex]1:2[/tex]
We appreciate your visit. Hopefully, the answers you found were beneficial. Don't hesitate to come back for more information. Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. Stay curious and keep coming back to Westonci.ca for answers to all your burning questions.
