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

Answer:

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

Step-by-step 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 $x=\frac{x_{1}m_{2}+x_{2}m_{1}}{m_{1}+m_{2}},y=\frac{y_{1}m_{2}+y_{2}m_{1}}{m_{1}+m_{2}}$

* 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)

∴ $x=\frac{(5)(3)+(-1)(1)}{1+3}=\frac{15+(-1)}{4}=\frac{14}{4}=3.5$

∴ $y=\frac{(8)(3)+(4)(1)}{1+3}=\frac{24+4}{4}=\frac{28}{4}=7$

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