Question

Find that coordinates of P that partitions directed line segment AB in a ratio of 1:3. A (-1, 2) B (7, 14) a (-1, 5) b (1, -5) c (1,5) d (5, 1)

Answer 1

Hence the coordinate of P are (5,13.5).

Explanation:

Given:

The line segment AB with point A≡(-1,2) and B≡(7,14)

To Find :

A point p coordinates as it divides seg AB in ratio of 1:3.

Solution:

Now we know the formula for the directed line segment as with ratio a:b

and coordinates of end points (x1,y1)and(x2,y2)

hence here values are ,

a=1 ,b=3 and x1=-1,y1=2 x2=7,y2=14

P≡[{(a*x1+b*x2)}/(a+b),{(a*y1+b*y2)}/(a+b)]

P≡[{(1*-1+3*7)}/(4),{(1*2+14*3)}/4]

p≡(20/4,54/4)

P≡(5,13.5)

Hence the coordiante of the P on directed line is at (5,13.5) as it divides in 1:3 ratio.