The line segment joining the points (3,-1) and (-6, 5) is trisected. The coordinates of point oftrisection are
Answers
Step-by-step explanation:
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}(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})(
m+n
mx
2
+nx
1
,
m+n
my
2
+ny
1
)
\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+2
1(−6)+2(3)
,
1+2
1(5)+2(−1)
)
=\displaystyle(\frac{0}{3},\frac{3}{3})=(
3
0
,
3
3
)
=\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+1
2(−6)+1(3)
,
2+1
2(5)+1(−1)
)
=\displaystyle(\frac{-9}{3},\frac{9}{3})=(
3
−9
,
3
9
)
=\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).