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Answers
Let the given points be A(2,−2) & B(−7,4)
P & Q are two points on AB such that
AP=PQ=QB
Let k=AP=PQ=QB
Hence comparing AP & PB
AP=k
PB=PQ+QB
=k+k=2k
Hence, ration of AP & PB =
2mm
=
2
1
Thus P divides AB in the ratio 1:2
Finding P
Let P(x,y)
Hence,
m
1
=1, m
2
=2
And for AB
x
1
=2, x
2
=−2
y
1
=−7, y
2
=4
x=
m
1
+m
2
m
1
x
2
+m
2
x
1
=
1+2
1×(−7)+2×2
=
3
−7+4
=−1
y=
m
1
+m
2
m
1
x
2
+m
2
x
1
=
1+2
1×4+2×(−2)
=
3
4−4
=0
Hence, point P is P(-1,0)
Similarly,
Point A divides AB in the ratio AQ & QB
=
QB
AQ
=
QB
AP+PQ
=
k
k+k
=
1
2
=2:1
Finding Q
Let Q(x,y)
Hence,
m
1
=2, m
2
=1
x
1
=2, x
2
=−2
y
1
=−7, y
2
=4
x=
m
1
+m
2
m
1
x
2
+m
2
x
1
=
1+2
2×(−7)+1×2
=
3
−14+2
=−4
y=
m
1
+m
2
m
1
x
2
+m
2
x
1
=
1+2
2×4+1×(−2)
=
3
8−2
=2
Hence, point Q is Q(-4,2)