Question

The line segment joining the points 3 - 1 and - 65 is trisected the coordinates of the point of trisection are

Answer 1

Answer:

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Step-by-step explanation:

Answer:

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

Step-by-step explanation:

\textbf{Concept:}Concept:

\text{The co ordinates of the point which divides the line segment joining}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}(x1,y1) and (x2,y2) internally in the ratio m:n is

\displaystyle\bf(\frac{mx_2+nx_1}{m+n},\frac{my_2+ny_1}{m+n})(m+nmx2+nx1,m+nmy2+ny1)

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

\text{Then, }Then, 

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

\text{The coordinates of P are}The coordinates of P are

\displaystyle(\frac{1(-6)+2(3)}{1+2},\frac{1(5)+2(-1)}{1+2})(1+21(−6)+2(3),1+21(5)+2(−1))

=\displaystyle(\frac{0}{3},\frac{3}{3})=(30,33)

=\displaystyle(0,1)=(0,1)

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

\text{The coordinates of Q are}The coordinates of Q are

\displaystyle(\frac{2(-6)+1(3)}{2+1},\frac{2(5)+1(-1)}{2+1})(2+12(−6)+1(3),2+12(5)+1(−1))

=\displaystyle(\frac{-9}{3},\frac{9}{3})=(3−9,39)

=\displaystyle(-3,3)=(−3,3)

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