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Rotated Tangent for $(5,-1)$

TRIG-GBJWKD

The line segment from the origin containing the point $(5,-1)$ is rotated about the origin $\pi$ radians.

Determine the tangent of the new angle formed between the line segment from the origin that contains the new coordinate and the positive $x$-axis.

A

$-\cfrac { 1 }{ 5 }$

B

$\cfrac { 1 }{ 5 }$

C

$-\ { 5 }$

D

$-\cfrac { 5\sqrt { 26 } }{ 26 }$

E

$-\cfrac { \sqrt { 26 } }{ 5 }$