Question

 If a point P divides the line segment joining the points A( 4, -3 ) and B ( 8, 5 ) in the ratio 3:1 then the co ordintaes of point P are ​

Answer 1

Answer:

(7 , 3)

Step-by-step explanation:

Given,

A = (4 , - 3)

B = (8 , 5)

Ratio = 3 : 1

m : n = 3 : 1

To Find :-

Co-ordinates of point 'P'

Formula Required :-

Section(Internal division) Formula :-

$(x,y)=\left(\dfrac{mx_2+nx_1}{m+n},\dfrac{my_2+ny_1}{m+n}\right)$

Solution :-

m : n = 3 : 1

A = (4 , - 3)

Let,

x_1 = 4 , y_1 = - 3

B = (8 , 5)

Let,

x_2 = 8 , y_2 = 5

Substituting the values in the formula :-

$P=\left(\dfrac{3(8)+1(4)}{3+1},\dfrac{3(5)+1(-3)}{3+1}\right)$

$=\left(\dfrac{24+4}{4},\dfrac{15-3}{4}\right)$

$=\left(\dfrac{28}{4},\dfrac{12}{4}\right)$

Cancelling in '4' table :-

= (7 , 3)

∴ Co-ordinates of 'P' = (7 , 3).

Answer 2

$▄︻デanswer══━一 ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ \: \: \: \: \: \: \: ‎ ‎ ‎⁍ ‎ ‎$

$using \: section \: formula$

$Here, \\ x_{1} = 4, \: y_{1} = - 3, \: x_{2} = 8, \: y_{2} = 5, \\m = 3, \: n = 1$

$p = (\frac{8(3)+4(1)</p><p>}{3 + 1} , \frac{5(3)+(−3)1}{3 + 1})$

$p = ( \frac{24 + 4}{4}, \frac{15 - 3}{4} </p><p>)$

$p = ( \frac{28}{4} </p><p>,\frac{12}{4} </p><p>)$

$P=(7,3)$