If square PQRS is reflected across the x axies to create P,Q,R,S what is the permiter
The perimeter of the reflected square will be the same as the original square.
If the original square PQRS has side length x, then the perimeter is 4x.
When the square is reflected across the x-axis, the new square P'Q'R'S' will have the same side length x.
Therefore, the perimeter of the reflected square P'Q'R'S' will also be 4x.
To find the perimeter of the reflected square PQRS, we need to determine the length of each side. Since it is a reflection across the x-axis, the x-coordinates of the vertices will remain the same, while the y-coordinates will be negated.
Let's say the side length of the original square PQRS is 'a'.
The coordinates of the original square are:
P(a, a)
Q(a, -a)
R(-a, -a)
S(-a, a)
For the reflected square P'Q'R'S', the y-coordinates will become negative. Therefore, the coordinates of the reflected square are:
P'(a, -a)
Q'(a, a)
R'(-a, a)
S'(-a, -a)
Using the coordinates, we can calculate the length of each side:
Side PQ: Distance between P(a, a) and Q(a, -a)
= |-a - a| = 2a
Side QR: Distance between Q(a, -a) and R(-a, -a)
= |-a - (-a)| = 0
Side RS: Distance between R(-a, -a) and S(-a, a)
= |a - (-a)| = 2a
Side SP: Distance between S(-a, a) and P(a, a)
= |a - a| = 0
Since sides QR and SP have length 0, we can ignore them in the perimeter calculation.
Therefore, the perimeter of the reflected square PQRS' is:
2a + 2a = 4a.
Hence, the perimeter of the reflected square PQRS' is 4a.