Answer: The correct option is (B) (b - a) units.
Step-by-step explanation: Given that M and N are the mid-points of RT and ST.
We are to find the length of MN.
As shown in the figure,
the co-ordinates of the point T are (2c, 2d),
the co-ordinates of the point S are (2b, 0),
and
the co-ordinates of the point R are (2c, 2d).
Since M is the mid-point of TR, so the co-ordinates of M are
[tex]\left(\dfrac{2c+2a}{2},\dfrac{2d+0}{2}\right)=(c+a,d).[/tex]
Also, N is the mid-point of TS, the co-ordinates of N are
[tex]\left(\dfrac{2c+2b}{2},\dfrac{2d+0}{2}\right)=(c+b,d).[/tex]
Therefore, the length of the line segment MN calculated using distance formula will be
[tex]MN=\sqrt{(c+b-c-a)^2+(d-d)^2}=\sqrt{(b-a)^2}=b-a.[/tex]
Thus, the required length of MN is (b - a) units.
Option (B) is correct.
