21. The point(0, 2) divides the join of points (1,3) and (a, b) in the ratio 1:2 internally.
Find the values of a and b.
Answers
Answer:
the point at the point that will be presenting divided by the joint of the two points and 1 upon 3 and the wide radius one account to enquiry find the value of the ap is equal to 3 into one
Answer:
Medium
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 P(−1,k) divides the line segment AB joining the points A(−3,10) and B(6,−8) in the ratio m:n, then using section formula we get,
P=(
m+n
mx
2
+nx
1
,
m+n
my
2
+ny
1
)
⇒(−1,k)=(
m+n
(m×6)+(n×−3)
,
m+n
(m×−8)+(n×10)
)
⇒(−1,k)=(
m+n
6m−3n
,
m+n
−8m+10n
)
⇒−1=
m+n
6m−3n
⇒−1(m+n)=6m−3n
⇒−m−n=6m−3n
⇒6m+m=3n−n
⇒7m=2n
⇒
n
m
=
7
2
⇒m:n=2:7
Hence, the point (−1,k) divides the line segment joining the points (−3,10) and (6,−8) in the ratio 2:7.