Question

Given xy=1, write the equation that indicates a reflection across the origin. Also, write another equation indicating a reflection across the line y=x

Answer 1

look at the first point (a,b) in the first quadrant and if you reflect the point the y-axis tt is reflected to the second quadrant point (−a, b).
if you reflect (a, b) about the x-axis, then it is reflected to the fourth quadrant point (a, −b).
but if we relect on the origin then it is relfected to the third qudrant