Answer: The correct option is (B) x = 2.5 units.
Step-by-step explanation: Given that line segment ST is dilated to create line segment S'T' using the dilation rule DQ, 2.25.
Also, SQ = 2 units, TQ = 1.2 units, TT'=1.5, SS' = x.
We are to find the value of x, the distance between points S' and S.
Since the line ST is dilated to S'T' with center of dilation Q, so the triangles STQ and S'T'Q must be similar.
We know that the corresponding sides of two similar triangles are proportional.
So, from ΔSTQ and ΔS'T'Q, we get
\(\dfrac{SQ}{S'Q}=\dfrac{TQ}{T'Q}\\\\\\\Rightarrow \dfrac{SQ}{SQ+S'S}=\dfrac{TQ}{TQ+TT'}\\\\\\\Rightarrow \dfrac{2}{2+x}=\dfrac{1.2}{1.2+1.5}\\\\\\\Rightarrow \dfrac{2}{2+x}=\dfrac{1.2}{2.7}\\\\\\\Rightarrow \dfrac{2}{2+x}=\dfrac{12}{27}\\\\\\\Rightarrow 54=24+12x\\\\\Rightarrow 12x=54-24\\\\\Rightarrow 12x=30\\\\\Rightarrow x=2.5.\)
Thus, the required value of x is 2.5 units.
Option (B) is correct.
