The point `p(3,4)` undergoes a reflection in the X-axis followed by a reflection in the y-axis. Show that their combined effect is the same as the single reflection of p(3,4) in the orign.

Explanation

let `p_(1) (x_(1),y_(1)` be the image of p (3,4) after reflection in the X-axis then,
`[(,x_(1)),(,y_(1))]=[(1,0),(0,-1)][(,3),(,4)]=[(,3),(,-4)]`
therefore, the image of p(3,4) after reflection in the X-axis is (3,4)

Now, let `p_(2) (x_(2),y_(2))` be the image of `p_(1)(3,-4)` after reflection in the y-axis, then
`[(,x_(2)),(,y_(2))]=[(-1,0),(0,-1)][(,3),(,-4)]=[(,-3),(,-4)]`
therefore the image of `p_(1)(3,-4)` after reflection in the Y-axis is `p_(2)(-3,-4)` be the image of `p(3,4)` in the origin O. then
`[(,x_(3)),(,y_(3))]=[(-1,0),(0,-1)][(,3),(,4)]=[(,-3),(,-4)]`
therefore the image of `p(3,4)` after reflection in the origin is `p_(3)(-3,-4)`. It is clear that `p_(2)=p_(3)`
Hence, the image of `p_(2)` of often successive reflection in their X-axis and Y-axis is the same as `p_(3)`, which is single reflction of p in the origin.