Question

Find the point of trisection of the line segment AB, where A (-6, 11) and B (10, -3).

Answer 1

$\textbf{Given:}$

$A(-6,11)\;\text{and}\;B(10,-3)$

$\textbf{To find:}$

$\text{Point of trisection of line segment AB}$

$\textbf{Solution:}$

$\text{Let P and Q be the points of trisection of line segment AB}$

$\text{Then, P and Q divide the line segment AB internally}$

$\text{in the ratio 1:2 and 2:1 respectively}$

$\text{Since P divides AB internally in the ratio 1:2, we have}$

$P\,(\,\dfrac{mx_2+nx_1}{m+n},\dfrac{my_2+ny_1}{m+n}\,)$

$P\,(\,\dfrac{1(10)+2(-6)}{1+2},\dfrac{1(-3)+2(11)}{1+2}\,)$

$P\,(\,\dfrac{10-12}{3},\dfrac{-3+22}{3}\,)$

$\implies\boxed{\bf\,P\,(\,\dfrac{-2}{3},\dfrac{19}{3}\,)}$

$\text{Since Q divides AB internally in the ratio 2:1, we have}$

$Q\,(\,\dfrac{mx_2+nx_1}{m+n},\dfrac{my_2+ny_1}{m+n}\,)$

$Q\,(\,\dfrac{2(10)+1(-6)}{2+1},\dfrac{2(-3)+1(11)}{2+1}\,)$

$Q\,(\,\dfrac{20-6}{3},\dfrac{-6+11}{3}\,)$

$\implies\boxed{\bf\,Q\,(\,\dfrac{14}{3},\dfrac{5}{3}\,)}$

Find more:

The line segment joining the points (3,-1) and (-6,5) is trisected. find the coordinate of the point of trisection.

https://brainly.in/question/8416219

$\text{}$

Answer 2

Answer:

answer is :-

let answer be x

let answer2 be y

By further solving we get,

x+y=answer

answer + answer = answer

Hence Proved,

question is wrong