Answer:
A and D
Step-by-step explanation:
We are given that
(3/4,2/3),(1/4,1),(1,1/2) and (1/2,1)
[tex]x_1=\frac{3}{4}[/tex]
[tex]y_1=\frac{2}{3}[/tex]
[tex]x_2=\frac{1}{4},y_2=1[/tex]
[tex]x_3=1,y_3=\frac{1}{2}[/tex]
[tex]x_4=\frac{1}{2},y_4=1[/tex]
k=[tex]\frac{1}{2}[/tex]
Direct proportion:
[tex]\frac{x}{y}=k[/tex]
Inverse proportion:[tex]xy=k[/tex]
[tex]\frac{x_1}{y_1}=\frac{3}{4}\times \frac{3}{2}=\frac{9}{8}\neq \frac{1}{2}[/tex]
Therefore, it is not in direct proportion.
[tex]\frac{1}{4\times 2}=\frac{1}{8}\neq\frac{1}{2}[/tex]
[tex]\frac{1}{\frac{1}{2}}=2\neq \frac{1}{2}[/tex]
[tex]x_1y_1=\frac{3}{4}\times \frac{2}{3}=\frac{1}{2}[/tex]
[tex]x_2y_2=\frac{1}{4}\times 2=\frac{1}{2}[/tex]
[tex]x_3y_3=1\times \frac{1}{2}=\frac{1}{2}[/tex]
[tex]x_4y_4=\frac{1}{2}\times 1=\frac{1}{2}[/tex]
Therefore, [tex]xy=k=\frac{1}{2}[/tex]
Hence, the given points form an inverse variation .
[tex]xy=\frac{1}{2}[/tex]
[tex]y=\frac{1}{2x}[/tex]
Option A and D is true.
