Answer: The required length of the segment AA' is 11 units.
Step-by-step explanation: Given that the point A(5, 11) is reflected across the X-axis.
We are to find the length of the segment AA'.
We know that
if a point (x, y) is reflected across X-axis, then its co-ordinates becomes (x, -y).
So, after reflection, the co-ordinates of the point A(5, 11) becomes A'(5, -11).
Now, we have the following distance formula :
The DISTANCE between two points P(a, b) and Q(c, d) gives the length of the segment PQ as follows :
[tex]PQ=\sqrt{(c-a)^2+(d-b)^2}.[/tex]
Therefore, the length of the segment AA' is given by
[tex]AA'=\sqrt{(5-5)^2+(-11-11)^2}=\sqrt{11^2}=11.[/tex]
Thus, the required length of the segment AA' is 11 units.
