(1) Find the coordinates of the points of trisection of the line segment joining the
(it) The line segment joining the points (3,-4) and (1, 2) is trisected at the points
coordinates of the point P.
4
points (3, -3) and (6, 9).
1,9 respectively, find the
5
and Q. If the coordinates of P and Q are (p, -2) and
3
values of p and g.
A (2) and B(
51) is divided
Answers
Answer:
p = 7 / 3
q = 0
Step-by-step explanation:
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