Answer with explanation:
The coordinates of vertices of Rectangle A B CD which lies in first Quadrant
=A(1,1),B(1,3),C(4,3) and D(4,1).
We have to find set of reflections which will carry rectangle ABCD onto itself.
Option-1:
When we reflect the rectangle along y axis,the rectangle moves in second Quadrant,and when it is reflected through x axis,it goes in Third Quadrant,and when it is reflected through y axis, the rectangle get transferred into fourth quadrant.This set of reflection would not carry rectangle ABCD onto itself.
Option-2:
When we reflect the rectangle along x axis,the rectangle moves in fourth Quadrant, and when it is reflected through y axis,it goes in Third Quadrant,and when it is reflected through y axis, the rectangle get transferred into fourth quadrant.This set of reflection would not carry rectangle ABCD onto itself.
Option-3
When we reflect the rectangle through x axis, the rectangle moves in fourth quadrant, having vertices A(1,-1),B(1, -3),C(4,-3) and D(4,-1).And when it is reflected through line y=x,the coordinates of rectangle becomes which goes into second quadrant A(-1,1),B(-3,1),C(-3,4) and D(-1,4).Now when the rectangle is reflected through x axis it moves into third Quadrant having vertices A(-1,-1),B(-3,-1),C(-3,-4) and D(-1,-4).Reflecting the rectangle along line , y=x takes it to third Quadrant having vertices A(-1,-1),B(-1,-3),C(-4,-3) and D(-4,-1).This set of reflection would not carry rectangle ABCD onto itself.
Option-4
Reflecting the rectangle along line , y=x gives the vertices of reflected rectangle A(1,1),B(3,1),C(3,4) and D(1,4).Now reflecting this rectangle through x axis takes it to fourth Quadrant having Vertices A(1,-1),B(3,-1),C(3,-4) and D(1,-4).Then reflecting through ,y=x ,takes this rectangle to A(-1,1),B(-1,3),C(-4,3) and D(-4,1),that is into second quadrant.Then reflecting through y axis, takes it to first Quadrant.So, This set of reflection would carry rectangle ABCD onto itself.
Option D:⇒ y=x, x-axis, y=x, y-axis