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

B

Explanation:

If point
`O(x_O,y_O)` divides the segment CD with endpoints at
`C(x_C,y_C)` and
`D(x_D,y_D)` in the ratio
`m:n,` then

`x_O=(nx_C+mx_D)/(m+n)\\ \\y_O=(ny_C+my_D)/(m+n)`

In your case,

`x_C=-4\\ \\y_C=3\\ \\x_D=8\\ \\y_D=-1\\ \\m:n=2:3,`

then

`x_O=(3\cdot (-4)+2\cdot 8)/(2+3)=(-12+16)/(5)=(4)/(5)\\ \\y_O=(3\cdot 3+2\cdot (-1))/(2+3)=(9-2)/(5)=(7)/(5)`