Find the corcinate of point of line
joining point (2, 3) and (4, 6)
which diveds the ratio 1:3 internaly
Answers
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.
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: