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)

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

[tex]x_O=\dfrac{nx_C+mx_D}{m+n}\\ \\y_O=\dfrac{ny_C+my_D}{m+n}[/tex]

In your case,

[tex]x_C=-4\\ \\y_C=3\\ \\x_D=8\\ \\y_D=-1\\ \\m:n=2:3,[/tex]

then

[tex]x_O=\dfrac{3\cdot (-4)+2\cdot 8}{2+3}=\dfrac{-12+16}{5}=\dfrac{4}{5}\\ \\y_O=\dfrac{3\cdot 3+2\cdot (-1)}{2+3}=\dfrac{9-2}{5}=\dfrac{7}{5}[/tex]

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)

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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)