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

(2.5 , 0)

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=((m)/(m+n))(x_2-x_1)+x_1$ , y=((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=((1)/(1+3))(-5-5)+5\\=((1)/(4))(-10)+5\\=(-10)/(4)+5\\\\x=2.5`

Similarly:

`y=((1)/(1+3))(3-(-1))+(-1)\\=((1)/(4))(4)-1\\=1-1\\y=0`

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