Question

Segment CD has endpoints (-4, 3) and (8, -1). Find the coordinates of the point that divides the line segment directed from C to D in the ratio of 2:3. A) ( -6 5 , 26 5 ) B) ( -4 5 , 7 5 ) C) ( 1 5 , 13 5 ) D) ( 16 5 , 3 5 )

Answer 1

`A(0.8,\ 1.4)\ \text{or }\ A\left((4)/(5),(7)/(5)\right)`

Explanation:

If point
`A(x,y)` divides the segment with endpoints
`C(x_1,y_1)` and
`D(x_2,y_2)` in the ratio
`m:n,`

then

`x=(nx_1+mx_2)/(m+n)\\ \\y=(ny_1+my_2)/(m+n)`

In your case,

`C(-4,3)\\ \\D(8,-1)\\ \\m:n=2:3`

then

`x=(3\cdot (-4)+2\cdot 8)/(2+3)=(-12+16)/(5)=(4)/(5)=0.8\\ \\y=(3\cdot 3+2\cdot (-1))/(2+3)=(9-2)/(5)=(7)/(5)=1.4`

Thus,

`A(0.8,\ 1.4)\ \text{or }\ A\left((4)/(5),(7)/(5)\right)`