As shown in the figure, let $\mathrm { Q } _ { 1 }$ be the point where the tangent line to the circle $x ^ { 2 } + y ^ { 2 } = 1$ at point $\mathrm { P } _ { 1 }$ meets the $x$-axis. The area of triangle $\mathrm { P } _ { 1 } \mathrm { OQ } _ { 1 }$ is $\frac { 1 } { 4 }$. Let $\mathrm { P } _ { 2 }$ be the point obtained by rotating $\mathrm { P } _ { 1 }$ about the origin O by $\frac { \pi } { 4 }$, and let $\mathrm { Q } _ { 2 }$ be the point where the tangent line at $\mathrm { P } _ { 2 }$ meets the $x$-axis. What is the area of triangle $\mathrm { P } _ { 2 } \mathrm { OQ } _ { 2 }$? (Here, point $\mathrm { P } _ { 1 }$ is in the first quadrant.) [3 points] (1) 1 (2) $\frac { 5 } { 4 }$ (3) $\frac { 3 } { 2 }$ (4) $\frac { 7 } { 4 }$ (5) 2
As shown in the figure, let $\mathrm { Q } _ { 1 }$ be the point where the tangent line to the circle $x ^ { 2 } + y ^ { 2 } = 1$ at point $\mathrm { P } _ { 1 }$ meets the $x$-axis. The area of triangle $\mathrm { P } _ { 1 } \mathrm { OQ } _ { 1 }$ is $\frac { 1 } { 4 }$. Let $\mathrm { P } _ { 2 }$ be the point obtained by rotating $\mathrm { P } _ { 1 }$ about the origin O by $\frac { \pi } { 4 }$, and let $\mathrm { Q } _ { 2 }$ be the point where the tangent line at $\mathrm { P } _ { 2 }$ meets the $x$-axis. What is the area of triangle $\mathrm { P } _ { 2 } \mathrm { OQ } _ { 2 }$? (Here, point $\mathrm { P } _ { 1 }$ is in the first quadrant.) [3 points]\\
(1) 1\\
(2) $\frac { 5 } { 4 }$\\
(3) $\frac { 3 } { 2 }$\\
(4) $\frac { 7 } { 4 }$\\
(5) 2