If you reflect rectangle abcd across x-axis, what will be the coordinates of a′ and c′?

Solution:A rectangle  ABCD reflected across x-axis, what will be the coordinates of A′ and C′.When a polygon is reflected then the two image and preimage are congruent.

Distance from x axis i.e between image and preimage is same.  

There are six possibilities:

1. If rectangle ABCD lies fully in first quadrant.→ reflected across X axis.

All coordinates of new rectangle A'B'C'D' lies in fourth quadrant i.e (x, -y).

2. If rectangle ABCD lies fully in second quadrant.→ All coordinates of new rectangle A'B'C'D' lies in Third quadrant i.e (-x, -y).

3. If two vertices i.e A and D  lie in first quadrant and other two B and C lie in second quadrant→The coordinates of A' and D' will be in fourth quadrant i.e (x, -y) and coordinates of B' and C' will be in third quadrant       (-x,-y).

Similarly if rectangle ABCD is in third quadrant the whole rectangle will lie in first quadrant, the coordinates of A and C will be in first quadrant i.e (x,y).

If rectangle ABCD is fully in fourth quadrant the whole rectangle will lie in second quadrant, the coordinates of A and C will be in second quadrant i.e (-x,y).

If two vertices i.e A and D  lie in third quadrant and other two B and C lie in fourth quadrant→The coordinates of A' and D' will be in first quadrant i.e (x, y) and coordinates of B' and C'will be in second quadrant       (-x,-y).