In what ratio is the line segment joining (-3, -1) and (-8, -9) divided at the point (-5, -21 /5)?
Answers
2 : 3 ratio is the line segment joining (-3, -1) and (-8, -9) divided at the point (-5, -21/5)
using section formula,
x = (λx₂ + x₁)/(λ + 1) , y = (λy₂ + y₁)/(λ + 1)
let (-5, -21/5) is dividing λ : 1 ratio of line joining the points (-3, -1) and (-8, -9)
so, -5 = {λ × -8 + (-3)}/(λ + 1)
⇒-5λ - 5 = -8λ - 3
⇒3λ = 2
⇒λ = 2/3
you can verify it using y = (λy₂ + y₁)/(λ + 1)
⇒-21/5 = {λ × -9 + (-1)}/(λ + 1)
⇒-21λ - 21 = -45λ -5
⇒24λ = 16
⇒λ = 2/3
hence ratio is 2 : 3
Answer:
Solution
verified
Verified by Toppr
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
)
Here, x
1
=−3,y
1
=−1,x
2
=−8,y
2
=−9
=(
m+n
mx
2
+nx
1
,
m+n
my
2
+ny
1
)=(−5,
5
−21
)
⇒
m+n
m(−8)+n(−3)
=−5
⇒−8m−3n=−5m−5n
⇒−8m+5m=3n−5n
⇒−3m=−2n
⇒
n
m
=
3
2
⇒m:n=2:3
Hence, the point (−5,
5
−21
) divides the line segment in the ratio 2:3.