Answer:
The coordinates of the point that divides the line segment directed from A to B in the ratio of 1:3 is P ( 2 , 2.25 ).
Step-by-step explanation:
Given:
Let Point P ( x , y ) divides Segment Am in the ratio 1 : 3 = m : n (say)
point A( x₁ , y₁) ≡ ( 1 , 2)
point B( x₂ , y₂) ≡ (5 , 3)
To Find:
point P( x , y) ≡ ?
Solution:
IF a Point P divides Segment AB internally in the ratio m : n, then the Coordinates of Point P is given by Section Formula as
[tex]x=\frac{(mx_{2} +nx_{1}) }{(m+n)}\\ \\and\\\\y=\frac{(my_{2} +ny_{1}) }{(m+n)}\\\\[/tex]
Substituting the values we get
[tex]x=\frac{(1\times 5 +3\times 1) }{(1+3)}\\ \\and\\\\y=\frac{(1\times 3 +3\times 2) }{(1+3)}\\\\\therefore x = \frac{8}{4}=2 \\\\and\\\therefore y = \frac{9}{4}=2.25 \\\\\\\therefore P(x,y) = (2 , 2.25)[/tex]
The coordinates of the point that divides the line segment directed from A to B in the ratio of 1:3 is P ( 2 , 2.25 ).
Answer:
2, 9/4
Step-by-step explanation:
(2, 9/4)
(mx2 + nx1)
(m + n)
,
(my2 + ny1)
(m + n)
Where the point divides the segment internally in the ratio m:n
((1)(5) + (3)(1))
(1 + 3)
,
((1)(3) + (3)(2))
(1 + 3)
= 2,
9
4
