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

Answer:

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

Step-by-step 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

$x=\dfrac{nx_1+mx_2}{m+n}\\ \\y=\dfrac{ny_1+my_2}{m+n}$

In your case,

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

then

$x=\dfrac{3\cdot (-4)+2\cdot 8}{2+3}=\dfrac{-12+16}{5}=\dfrac{4}{5}=0.8\\ \\y=\dfrac{3\cdot 3+2\cdot (-1)}{2+3}=\dfrac{9-2}{5}=\dfrac{7}{5}=1.4$

Thus,

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