Question

Bो
(a) Find the co-ordinates of the
point of trisection of the line
segment joining (
3, -3) and (9,9)​

Answer 1

$\textbf{Given:}$

$\textsf{Points are (3,-3) and (9,9)}$

$\textbf{To find:}$

$\textsf{Point of trisection of the line segment joining the given points}$

$\textbf{Solution:}$

$\textsf{Let the given points be A(3,-3) and B(9,9)}$

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

$\textsf{Since P divides AB internally in the ratio 1:2, coordinates of P are}$

$\mathsf{\left(\dfrac{mx_2+nx_1}{m+n},\dfrac{my_2+ny_1}{m+n}\right)}$

$\mathsf{\left(\dfrac{1(9)+2(3)}{1+2},\dfrac{1(9)+2(-3)}{1+2}\right)}$

$\mathsf{\left(\dfrac{9+6}{3},\dfrac{9-6}{3}\right)}$

$\mathsf{\left(\dfrac{15}{3},\dfrac{3}{3}\right)}$

$\mathsf{(5,1)}$

$\textsf{Since Q divides AB internally in the ratio 2:1, coordinates of Q are}$

$\mathsf{\left(\dfrac{mx_2+nx_1}{m+n},\dfrac{my_2+ny_1}{m+n}\right)}$

$\mathsf{\left(\dfrac{2(9)+1(3)}{2+1},\dfrac{2(9)+1(-3)}{2+1}\right)}$

$\mathsf{\left(\dfrac{18+3}{3},\dfrac{18-3}{3}\right)}$

$\mathsf{\left(\dfrac{21}{3},\dfrac{15}{3}\right)}$

$\mathsf{(7,5)}$

$\textbf{Answer:}$

$\textsf{Points of trisection are (5,1) and (7,5)}$

$\textbf{Find more:}$

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

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

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