Question

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

Answer 1

Answer:

$\text{The points of trisection are (0,1) and (-3,3)}$

Step-by-step explanation:

$\textbf{Concept:}$

$\text{The co ordinates of the point which divides the line segment joining}$$\text{ (x_1,y_1) and (x_2,y_2) internally in the ratio m:n is}$

$\displaystyle\bf(\frac{mx_2+nx_1}{m+n},\frac{my_2+ny_1}{m+n})$

$\text{Let P and Q be the points of trisection of the line segment joining (3,-1) and (-6,5)}$

$\text{Then, }$

$\text{P divides AB internally in the ratio 1:2}$

$\text{The coordinates of P are}$

$\displaystyle(\frac{1(-6)+2(3)}{1+2},\frac{1(5)+2(-1)}{1+2})$

$=\displaystyle(\frac{0}{3},\frac{3}{3})$

$=\displaystyle(0,1)$

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

$\text{The coordinates of Q are}$

$\displaystyle(\frac{2(-6)+1(3)}{2+1},\frac{2(5)+1(-1)}{2+1})$

$=\displaystyle(\frac{-9}{3},\frac{9}{3})$

$=\displaystyle(-3,3)$

$\therefore\text{The points of trisection are (0,1) and (-3,3)}$

Find more:

Find the ratio in which the line x+3y-14=0 divides the line segment joining the points A(-2,4) B(3,7).

https://brainly.in/question/1594798#

Answer 2

Answer:

Step-by-step explanation:

0,3