Answer:
2:3
Step-by-step explanation:
Given: Points A(-3,-4) and B(2,0), point P(-1,-12/5)
To find: The ratio in which P divide AB
Solution:
We know that the coordinate of a point [tex](x,y)[/tex] dividing a line segment joining [tex](x_{1},y_{1}) \:\text{and} (x_{2},y_{2})[/tex] in the ratio m:n is given by
[tex]x=\frac{mx_{2}+nx_{1}}{m+n}[/tex], [tex]y=\frac{my_{2}+ny_{1}}{m+n}[/tex]
Now, let the ratio be k:1
Here, coordinate of P is [tex](-1,\frac{-12}{5} )[/tex]
So, [tex]-1=\frac{ k(2)+1(-3)}{k+1}[/tex]
[tex]-k-1=2k-3[/tex]
[tex]2k+k=3-1[/tex]
[tex]3k=2[/tex]
[tex]k=\frac{2}{3}[/tex]
Hence, the ratio is 2:3.
