Question

find the coordinates of the point which divides the join of (-1,7)and(4,-3) in the ratio 2:3............3Marks Question

Answer 1

A_________P_________B

( -1 , 7 ) ( x , y ) ( 4 , -3 )

Let AP : PB be m : n
and given :- m : n = 2 : 3


For Coordinate of P


$x = \frac{mx2 + nx2}{m + n}$


$x = \frac{2 \times 4 + 3 \times - 1}{2 + 3}$

$x = \frac{8 - 3}{5}$


$x = \frac{5}{5}$

x = 1


$y = \frac{my2 + ny1}{m + n}$


$y = \frac{2 \times - 3 + 3 \times 7}{5}$


$y = \frac{ - 6 + 21}{5}$

$y = \frac{15}{5}$

y = 3


So,

Coordinate of the point P which divide the line in ratio 2 : 3 is ( 1 , 3 )

Answer 2

x1,x2= -1,4
y1,y2= 7,-3
m1:m2= 2:3

P,Q = (m1x2+m2x1)÷m1+m2 ,
(m1y2+m2y1) ÷ m1+m2

= [2(4)+3 (-1)] ÷2+3 ,
[2 (-3)+3 (7)]÷ 2+3

= 8-3÷5, -6+21÷5
=1 , 3
P,Q= 1,3