Question

If A and B are (-2,-2) and (2, - 4) respectively. Find the co-ordinates of P
such that AP = 4/7 AB and P lies on line segment AB.​

Answer 1

Answer:

since P lies on line segment AB, mean P divides the line AB internally. Now we have to find the ratio in which P divides AB i.e. AP/PB

given

AP = (4/7) AB

AP/AB = 4/7

using dividendo

AP/AB-AP = 4/(7-4)

AP/PB = 4/3

hence m= 4, n = 3

now we know the coordinate of a point dividing a line segment joining two points (X1,y1) and (x2,y2) internally is given by

(mx2+nx1)/(m+n), (my2+ny1)/(m+n)

here (X1,y1) = (-2,-2) and (x2,y2) is (2,-4)

the coordinate of P is

(4*2+3*-2)/(4+3), (4*-4+3*-2)/(4+3)

= (8+6)/7, (-16-6)/7

= 14/7, -22/7

= (2, -22/7)