The average normal strains measured by a strain rosette at angles of $270,1050,$ and $2610$ counterclockwise from the horizontal x$-$axis at a point on the free surface of a plane stressed body $($ $=0\mathrm{.}3$ and E $=210$ GPa$)$ are, $+50$ $,+225$ $,$ and $-70$ $,$ respectively. Determine:

$($a$)$ The strain components x$,$ y$,$ and xy at the point.

$($b$)$ The principal strains, the maximum in$-$plane shearing strain at the point, and the angle $($relative to the vertical plane$)$ at which the maximum principal strain acts.

$($c$)$ The normal stresses $($x and y$)$ and the shearing stress $($xy$)$ at the point.

$($d$)$ The normal and shearing strain on a plane inclined at $30$o anticlockwise from the horizontal plane.