Question

the co-ordinates of a,b are (-2,-2), (2,-4).find p such that ap=3/7ab

Answer 1

hello
given
a=(-2,-2).
b=(2,-4).
ap=3/7ab
let us assume sample diagram
a(-2,-2). p( x,y). b(2,-4)
+---------------+----------------+
ap= 3/7(ap+pb)
7ap=3(ap+pb)
7ap=3ap+3pb
7ap-3ap= 3pb
4ap=3pb

ap/pb = 3/4

hence the point p divides ab in the ratio of 3:4

m1=3;m2=4

to find coordinates
x= (m1x2+m2x1)/m1+m2
=( 3×2+4×-2)/3+4
= ( 6-8)/7
x = -2/7

y= (m1y2+m2y1)/m1+m2
=(3×-4+4×-2)/3+4
=(-12-8)/7
= -20/7
hence the coordinates of p( x,y)= (-2/7,-20/7)

hope it will help