find the points of trisection of the line segment joining the point A 2,-2 and b -7,4
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Step-by-step explanation:
Let A and B be the points of trisection of the segment PQ, then
PA=AB=BQ⇒2PA=AQ
⇒
AQ
PA
=
2
1
⇒A divides the line segment PQ in the ratio 1:2 internally.
∴A=(
1+2
1×8+2×2
,
1+2
1×−14+2×0
,
1+2
1×3+2×−4
)
=(
3
8+4
,
3
−14+0
,
3
3−8
)
=(
3
12
,
3
−14
,
3
−5
)
∴A=(4,
3
−14
,
3
−5
)
Also,PA=AB=BQ⇒PB=2BQ
⇒
BQ
PB
=
1
2
⇒B divides the line segment PQ in the ratio 2:1 internally.
∴B=(
2+1
2×8+1×2
,
2+1
2×−14+1×0
,
2+1
2×3+1×−4
)
=(
3
16+2
,
3
−28+0
,
3
6−4
)
=(
3
18
,
3
−28
,
3
2
)
∴B=(6,
3
−28
,
3
2
)
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