Question

Given the points C(5, -1) and D(-5, 3), find the coordinates of the point P on directed line segment CD that partitions segment CD such that the ratio of CP to PD is 1:3

Answer 1

Answer:

(2.5 , 0)

Step-by-step explanation:

Given points C and D. the coordinates of point P that partitions CD such that CP:PD=m:n can be calculated using the formula:

$x=(\dfrac{m}{m+n})(x_2-x_1)+x_1 , y=(\dfrac{m}{m+n})(y_2-y_1)+y_1\\\\ Now, (x_1,y_1)=C(5,-1), (x_2,y_2)=D(-5,3), m:n=1:3\\Therefore:\\x=(\dfrac{1}{1+3})(-5-5)+5\\=(\dfrac{1}{4})(-10)+5\\=\dfrac{-10}{4}+5\\\\x=2.5$

Similarly:

$y=(\dfrac{1}{1+3})(3-(-1))+(-1)\\=(\dfrac{1}{4})(4)-1\\=1-1\\y=0$

Therefore, the coordinates of P is (2.5,0)