Physicists Know That If Each Edge of a Thin Conducting $$x _ { 1 } , x _ { 2 } , x _ { 3 } , \text { and } x _ { 4 }$$

Physicists know that if each edge of a thin conducting plate is kept at a constant temperature, then the
temperature at the interior points is the mean (average) of the four surrounding points equidistant from
the interior point. Use this principle in to find the temperature at points $$x _ { 1 } , x _ { 2 } , x _ { 3 } , \text { and } x _ { 4 }$$
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A) $x _ { 1 } = 42 ^ { \circ } \mathrm { F } ; x _ { 2 } = 47 ^ { \circ } \mathrm { F } ; x _ { 3 } = 49 ^ { \circ } \mathrm { F } ; x _ { 4 } = 54 ^ { \circ } \mathrm { F }$ ;
B) $x _ { 1 } = 42 ^ { \circ } \mathrm { F } ; x _ { 2 } = 46 ^ { \circ } \mathrm { F } ; x _ { 3 } = 50 ^ { \circ } \mathrm { F } ; x _ { 4 } = 54 ^ { \circ } \mathrm { F }$ ;
C) $x _ { 1 } = 45 ^ { \circ } \mathrm { F } ; x _ { 2 } = 47 ^ { \circ } \mathrm { F } ; x _ { 3 } = 49 ^ { \circ } \mathrm { F } ; x _ { 4 } = 51 ^ { \circ } \mathrm { F }$ ;
D) $x _ { 1 } = 45 ^ { \circ } \mathrm { F } ; x _ { 2 } = 46 ^ { \circ } \mathrm { F } ; x _ { 3 } = 50 ^ { \circ } \mathrm { F } ; x _ { 4 } = 51 ^ { \circ } \mathrm { F }$ ;