Welcome to Westonci.ca, the place where your questions are answered by a community of knowledgeable contributors. Experience the convenience of finding accurate answers to your questions from knowledgeable experts on our platform. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently.
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]
Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. Discover more at Westonci.ca. Return for the latest expert answers and updates on various topics.
