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,Line segment PQ is shown on a coordinate grid:


A coordinate grid is shown from positive 6 to negative 6 on the x-axis and from positive 6 to negative 6 on the y-axis. A line segment PQ is shown with Q as ordered pair negative 1, 3 and P as ordered pair negative 5, 3.


The line segment is rotated 270 degrees counterclockwise about the origin to form P'Q'. Which statement describes P'Q'?


P'Q' is two times the length of PQ.

P'Q' is equal in length to PQ.

P'Q' is half the length of PQ.

P'Q' is parallel to PQ.

Respuesta :

jolis1796

Answer:

P'Q' is equal in length to PQ.

Step-by-step explanation:

Before rotation

P(-5, 3)

Q(-1, 3)

we get the length

L = √((-1-(-5))²+(3-3)²) = √((-4)²+(0)²) = 4

After rotation

P'(3, 5)

Q'(3, 1)

we get the length

L' = √((3-3)²+(1-5)²) = √((0)²+(-4)²) = 4

we can say that   L = L' = 4

P'Q' is equal in length to PQ.