Answer :
The ratio of interest can be found for collinear points by considering only one of the coordinates. Let's look at the x-coordinates.
(Tx -Mx)/(Dx -Mx) = (1-(-3))/(9-(-3)) = 4/12 = 1/3
Then the ratio of interest is MT:MD = 1:3.
Answer: The required ratio is MT : TD = 1 : 2.
Step-by-step explanation: Given that the points M, T and D are collinear on line segment MD.
M is located at (-3,-5), T is located at (1,-3) and D is located at (9,1).
We are to find the ratio MT : TD.
Let us consider that
MT : TD = m : n.
We know that
the co-ordinates of a point that divides a line segment with end points (a, b) and (c, d) are given by
[tex]\left(\dfrac{mc+na}{m+n},\dfrac{md+nb}{m+n}\right).[/tex]
For the given situation, we have
[tex]1=\dfrac{m\times 9+n\times (-3)}{m+n}\\\\\\\Rightarrow m+n=9m-3n\\\\\Rightarrow 9m-m=n+3n\\\\\Rightarrow 8m=4n\\\\\Rightarrow 2m=n\\\\\Rightarrow \dfrac{m}{n}=\dfrac{1}{2}\\\\\Rightarrow m:n=1:2[/tex]
Thus, the required ratio is MT : TD = 1 : 2.