Find the corcinate of point of line
joining point (2, 3) and (4, 6)
which diveds the ratio 1:3 internaly
Answers
Answer:Given:-
A(x₁, y₁) = (2, 3)
B(x₂, y₂) = (4, 6)
m : n = 1 : 3 internally.
To find:-
P(α, β) = ?
Answer:-
We have to use the section formula for internal division. It says that,
If P(α, β) divides a line segment AB with A(x₁, y₁) and B(x₂, y₂) internally in the ratio m : n, then,
α = [(mx₂ + nx₁) / (m + n)]
β = [(my₂ + ny₁) / (m + n)]
According to the question, putting the values as,
x₁ = 2
y₁ = 3
x₂ = 4
y₂ = 6
m = 1
n = 3
Putting the values in the formula,
▪α = [(mx₂ + nx₁) / (m + n)]
→ α = [ {(1 × 4) + (3 × 2)} / (1 + 3) ]
→ α = [ {4 + 6} / 4 ]
→ α = 10/4
→ α = 2.5
And,
▪β = [(my₂ + ny₁) / (m + n)]
→ β = [ {(1 × 6) + (3 × 3)} / (1 + 3)]
→ β = [ {6 + 9} / {4} ]
→ β = 15/4
→ β = 3.75
So,
→ P(α, β) = (2.5, 3.75) Ans.
Step-by-step explanation:
Answer:
here's ur answer dude
Step-by-step explanation:
The coordinates of point when (x
1
,y
1
) and (x
2
,y
2
) are divided in m:n
(i) internally is (
m+n
mx
2
+nx
1
,
m+n
my
2
+ny
1
)
(ii) externally (
m−n
mx
2
−nx
1
,
m−n
my
2
−ny
1
)
Let the point be P(h,k)
(1) For internal division
h=
2+3
2(4)+3(−1)
=
5
5
=1
k=
2+3
2(−5)+3(2)
=
5
−4
⇒P(1,
5
−4
)
(2) For external division
h=
2−3
2(4)−3(−1)
=
−1
8+3
=−11
k=
2−3
2(−5)−3(2)
=
−1
−10−6
=16
⇒P(−11,16)