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