Answer:
We know that the section formula states that if a point P(x,y) lies on line segment AB joining the points A(x
1
,y
1
) and B(x
2
,y
2
) and satisfies AP:PB=m:n, then we say that P divides internally AB in the ratio m:n. The coordinates of the point of division has the coordinates
P=(
m+n
mx
2
+nx
1
,
m+n
my
2
+ny
1
)
Let C(1,1) divides the line segment AB joining the points A(−2,7) and B(x
2
,y
2
) in the ratio 3:2, then using section formula we get,
C=(
m+n
mx
2
+nx
1
,
m+n
my
2
+ny
1
)
⇒(1,1)=(
3+2
3x
2
+(2×−2)
,
3+2
3y
2
+(2×7)
)
⇒(1,1)=(
5
3x
2
−4
,
5
3y
2
+14
)
⇒1=
5
3x
2
−4
,1=
5
3y
2
+14
⇒5=3x
2
−4,5=3y
2
+14
⇒3x
2
=5+4,3y
2
=5−14
⇒3x
2
=9,3y
2
=−9
⇒x
2
=
3
9
,y
2
=−
3
9
⇒x
2
=3,y
2
=−3
Hence, the point B(x
2
,y
2
) is B(3,−3).
