Linear Function

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If the distance between (3, -2) and (4, a)  is the sqaure root of 7, find the exact value of a.

$\sqrt{(4-3)^2+(a--2)^2}=\sqrt7\\ (4-3)^2+(a--2)^2=7\\ 1+(a+2)^2=7\\ (a+2)^2=6\\ a+2=\pm\sqrt6\\ a=-2\pm\sqrt6\\ $