May I get some help I don't know if I'm right

Question

asked May 21, 2023 183k views

1 Answer

Alkey · Answer 1 · 2023-05-26T23:24:07+0000

The point C divides the line AB in ratio 3:2 means that,

Determine the coordinate of point B.

$\begin{gathered} (3.6,-0.4)=((3x-2\cdot6)/(3+2),(3y+2\cdot5)/(5)) \\ (3.6,-0.4)=((3x-12)/(5),(3y+10)/(5)) \end{gathered}$

Simplify the equation for x and y.

$\begin{gathered} (3x-12)/(5)=3.6 \\ 3x-12=3.6\cdot5 \\ 3x=18+12 \\ x=(30)/(3) \\ =10 \end{gathered}$

For y,

$\begin{gathered} -0.4=(3y+10)/(5) \\ 3y+10=-0.4\cdot5 \\ 3y=-2-10 \\ y=-(12)/(3) \\ =-4 \end{gathered}$

So coordinates of the point B are (10,-4).

Determine the coordinates of the point D which divide the line CB in 4:5 ratio.

$\begin{gathered} D(x,y)=((4\cdot10+5\cdot3.6)/(4+5),(4\cdot(-4)+5\cdot(-0.4))/(4+5)) \\ =((40+18)/(9),(-16-2)/(9)) \\ =((58)/(9),-2) \end{gathered}$

So coordinates of point D is (58/9,-2).