the line segment joining the points A(3,-4) and B(1,2) is trisected at points P and Q where P is nearer to A. find coordinates of P.
answer in detail. Don't spam.
Answers
the line segment joining the points A(3,-4) and B(1,2) is trisected at points P and Q where P is nearer to A. find coordinates of P.
Correct option is
B
p=7/3,q=0
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
please mark my ans as brainliest please