Answer:
(A)\(3.2=\sqrt{(4.5-2.5)^2+(y_{2}-3)^2}\)
Step-by-step explanation:
From the given figure, using the distance formula, we have
\(d=\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2}\)
We have the points that are \((2.5,3)\) and \((4.5,y_{2})\), thus
\(d=\sqrt{(4.5-2.5)^2+(y_{2}-3)^2}\)
Also, it is given that the value of d is 3.2, therefore the above equation becomes
\(3.2=\sqrt{(4.5-2.5)^2+(y_{2}-3)^2}\)
Upon solving the above equation, we get
\(3.2=\sqrt{(2.0)^2+(y_{2}-3)^2}\)
\(3.2=\sqrt{4.0+(y_{2}-3)^2}\)
Squaring on both the sides, we have
\(10.24=4.0+(y_{2}-3)\)
\(6.24=(y_{2}-3)^2\)
Taking square root on both sides, we get
\(2.49=y_{2}-3\)
\(y_{2}=5.49\)
Thus, the value of \(y_{2}\) is 5.49.
Hence, option A is correct.
