Question

The point A (5,11) is reflected across the x-axis. How long is the segment AA'?​

Answer 1

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 :

$PQ=\sqrt{(c-a)^2+(d-b)^2}.$

Therefore, the length of the segment AA' is given by

$AA'=\sqrt{(5-5)^2+(-11-11)^2}=\sqrt{11^2}=11.$

Thus, the required length of the segment AA' is 11 units.