Question

Find the coordinates of P so that P partitions the segment AB in the ratio 1:3 if A(5,8) and B(−1,4).

A. (-6.5, -9)

B. (-1.5, -1)

C. (3.5, 7)

D. (-4, -6)

Answer 1

The coordinates of point P are (3.5 , 7) ⇒ answer C

Explanation:

* Lets explain how to solve the problem

- If the point (x , y) divide a line whose endpoints are (x1 , y1) , (x2 , y2)

at ratio m1 : m2 from the point (x1 , y1), then the coordinates of the

point (x , y) are
`x=(x_(1)m_(2)+x_(2)m_(1))/(m_(1)+m_(2)),y=(y_(1)m_(2)+y_(2)m_(1))/(m_(1)+m_(2))`

* Lets solve the problem

∵ A is (5 , 8) and B is (-1 , 4)

∵ P divides AB in the ratio 1 : 3

∴ m1 = 1 and m2 = 3

- Let A = (x1 , y1) and B = (x2 , y2)

∴ x1 = 5 , x2 = -1 and y1 = 8 , y2 = 4

- Let P = (x , y)

∴
`x=((5)(3)+(-1)(1))/(1+3)=(15+(-1))/(4)=(14)/(4)=3.5`

∴
`y=((8)(3)+(4)(1))/(1+3)=(24+4)/(4)=(28)/(4)=7`

∴ The coordinates of point P are (3.5 , 7)