Question

find the coordinates of point which divides the join of (3, 6 )and (7, 4 )in the ratio 4 is to 5.

Answer 1

⤵️Sᴏʟᴜᴛɪᴏɴ:-

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 = {mx2 + nx2}{m + n}x= m+n

mx2+nx2

x = {4 + 3 - 1}{2 + 3}x= 2+3

2×4+3×−1

x = \{8 - 3}{5}x= 58−3

x = {5}{5}x= 55

x = 1

y = {my2 + ny1}

= {m + n}y= m+n

= my2+ny1

y = {2 - 3 + 37}{5}y= 5

2×−3+3×7

y = { - 6 + 21}{5}y= 5

−6+21

y = {15}{5}y= 5 15

y = 3

So,

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

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