Answer:
Therefore, the coordinates of point P(x ,y) are P ( 7 , 3 ) which divides the directed line segment AB into 3 : 4.Step-by-step explanation:
Given:
point A( x₁ , y₁) ≡ ( 0 ,-5)
point B( x₂ , y₂) ≡ (2 , 0)
Let point p( x , y ) divide Line AB in the ratio 3 : 4 i.e m : n
To Find:
P ( x, y ) = ?
Solution:
if point P( x , y) divide segment AB internally in the ratio m : n then the X coordinate and the Y coordinate is given by section formula:
[tex]x=\frac{(mx_{2} +nx_{1}) }{(m+n)}\\ \\and\\\\y=\frac{(my_{2} +ny_{1}) }{(m+n)}\\\\[/tex]
On substituting the above given values in section formula we get
[tex]x=\frac{(3\times 15 +4\times 1) }{(3+4)}\\ \\and\\\\y=\frac{(3\times 3 +4\times 3)}{(3+4)}\\\\\\x=\frac{49}{7}=7\\\\and\\\\y=\frac{21}{7}=3\\[/tex]
Therefore, the coordinates of point P(x ,y) are P ( 7 , 3 ) which divides the directed line segment AB into 3 : 4.
Answer:
(7, 3)
Step-by-step explanation:
Given that:
Let point P (a, b) divides the directed line segment AB¯¯¯¯¯ into a 3:4 ratio
So we have:
[tex]P(a,b)=[a=\frac{m\cdot x_2+n\cdot x_1}{m+n},b=\frac{m\cdot y_2+n\cdot y_1}{m+n}][/tex] , where m : n = 3 : 4
Let A(1 ,3) = [tex](x_1,y_1), (15,3)=(x_2,y_2), m=3\text{ and }n=4.[/tex]
Upon substituting coordinates of our given points in section formula we will get:
[tex]P(a,b)=[a=\frac{3\cdot 15+4\cdot 1}{3+4},b=\frac{3\cdot 3+4\cdot 3}{3+4}][/tex]
P(a, b) = (a = 7, b = 3)
Hope it will find you well.
