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).

i dont know sorry

step-by-step explanation:

the simplified form is

step-by-step explanation:

we want to simplify the expression,

let us change the middle bar to a normal division sign to obtain,

we multiply the first fraction by the reciprocal of the second fraction to obtain,

we factor to obtain,

we cancel the common factors to get,

we simplify to get,

the correct answer is b