Answer:
A) JK and LM will be parallel to each other.
Step-by-step explanation:
On reflection on [tex]y=x[/tex] line the x co-ordinate changes with y co-ordinate and y co-ordinate changes with x co-ordinate
[tex](x,y)\rightarrow (y,x)[/tex]
Points on line EF
[tex](0,6) , (-5,-2)[/tex]
On reflection of this line on [tex]y=x[/tex] the new points we get for line JK are
[tex](6,0),(-2,-5)[/tex]
Points on line GH
[tex](-4,9),(-9,1)[/tex]
On reflection on y=x line the new points we get for line LM are
[tex](9,-4),(1,-9)[/tex]
Slope of line JK
[tex]m=\frac{y_2-y_1}{x2-x1}\\m=\frac{(-5)-0}{(-2)-6} \\m=\frac{-5}{-8}=\frac{5}{8}[/tex]
Slope of line LM
[tex]m=\frac{y_2-y_1}{x2-x1}\\m=\frac{(-9)-(-4)}{1-9} \\m=\frac{-9+4}{-8}=\frac{-5}{-8}\\m=\frac{5}{8}[/tex]
For two line to be parallel, their slopes will be same.
[tex]m_{JK} =\frac{5}{8} , m_{LM}=\frac{5}{8}[/tex]
Since slopes of lines JK and LM are same therefore we can say that these are parallel to each other.
