Find the coordinates of a point P on the line segment joining A(7,3)A(7,3 )and B(7,−4) such that AP = 2/7AB
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Answer:
Using the section formula, if a point (x,y) divides the line joining the points (x
1
,y
1
) and (x
2
,y
2
) in the ratio m:n, then
(x,y)=(
m+n
mx
2
+nx
1
,
m+n
my
2
+ny
1
)
Since,
AP=
5
2
AB
⇒5AP=2(AP+PB)
⇒5AP=2AP+2PB
⇒3AP=2PB
⇒
PB
AP
=
3
2
⇒AP:PB=2:3
Therefore,
(x,y)=(
2+3
2×6+3×1
,
2+3
2×7+3×2
)
=(
5
15
,
5
20
)
=(3,4)
So, coordinates of point P is (3,4)
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