The line segment joining the points (3,-4)and (1,2)is
trisected at the points P and Q. If the coordinates of P and Q are (p,-2) and (5/3,q) respectively. Fimd the value of P and Q.
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Answer:
Suppose Points P and Q trisect the line segment joining the pointsA(3,−4) and B(1,2)
This means, P divides AB in the ratio 1:2 and Q divides it in the ratio 2:1
Using the section formula, if point (x,y) divides the line joining the points (x
1
,y
1
) and (x
2
,y
2
) internally in the ratio m:n, then(x,y)=(
m+n
mx
2
+nx
1
,
m+n
my
2
+ny
1
)
Substituting (x
1
,y
1
)=(3,−4) and (x
2
,y
2
)=(1,2) and m=1,n=2 in the section formula, we get the point P =(
1+2
1(1)+2(3)
,
1+2
1(2)+2(−4)
)=(
3
7
,−2)
Given. P(p,−2)=(
3
7
,−2)
=>p=
3
7
Substituting (x
1
,y
1
)=(3,−4) and (x
2
,y
2
)=(1,2) and m=2,n=1 in the section formula, we get the point Q =(
2+1
2(1)+1(3)
,
2+1
2(2)+1(−4)
)=(
3
5
,0)
Given. Q(
3
5
,0)=(
3
5
,q)
=>q=0
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