Answer:
Therefore the length of each side of square [tex]QRST[/tex] is [tex]9\ unit[/tex].
Step-by-step explanation:
Given that,
[tex]QRST[/tex] is a square.
The coordinate of point [tex]Q[/tex] is [tex](3.6,2.1)[/tex].
The coordinate of point [tex]R[/tex] is [tex](-5.4,2.1)[/tex].
Let, The coordinate of point [tex]S[/tex] is [tex](-5.4,y)[/tex] and the coordinate of point [tex]T[/tex] is [tex](3.6,y)[/tex].
Diagram of the square [tex]QRST[/tex] is shown below:
Now,
[tex]QR=\sqrt{(-5.4-3.6)^{2} +(2.1-2.1)^{2} }[/tex] [Distance Formula]
[tex]QR=\sqrt{(9)^{2} -(0)^{2} }[/tex]
[tex]=\sqrt{81}[/tex]
[tex]= 9\ unit[/tex]
Therefore the length of square [tex]QRST[/tex] is [tex]9\ unit.[/tex]
[tex]RS=\sqrt{(-5.4+5.4)^{2} +(y-2.1)^{2} }[/tex]
[tex]9=\sqrt{(0)^{2} +(y-2.1)^{2} }[/tex] [[tex]QR=RS[/tex], because [tex]QRST[/tex] is a square]
⇒ [tex]9=\sqrt{(y-2.1)^{2} }[/tex]
squaring both sides, we get
⇒[tex]81=(y-2.1)^{2}[/tex]
⇒ [tex](y-2.1)[/tex] [tex]=[/tex] ±[tex]9[/tex]
∴[tex]y=11.1[/tex]
The coordinate of point [tex]S[/tex] is [tex](-5.4,11.1)[/tex] and the coordinate of point [tex]T[/tex] is [tex](3.6,11.1)[/tex].
∵ [tex]QRST[/tex] is a square
∴[tex]QR=RS=ST=TQ=9\ unit[/tex]
Therefore the length of each side of square [tex]QRST[/tex] is [tex]9\ unit[/tex].
