How do you find the value of a given the points (a,2), (-3,3) with a distance of $sqrt2$ ?

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Answer 1 · 2017-07-26T17:43:13

$a=-4 or a=-2$

$d=sqrt((x_2-x_1)^2+(y_2-y_1)^2)$

$sqrt2=sqrt((-3-a)^2+(3-2)^2)$ $->$ plug in given values

$sqrt2=sqrt(9+6a+a^2+1)$ $->$ expand

$sqrt2=sqrt(a^2+6a+10)$ $->$ simplify

$2=a^2+6a+10$ $->$ remove radical by squaring both sides

$0=a^2+6a+8$ $->$ subtract $2$ from both sides

$0=(a+4)(a+2)$ $->$ factor

$0=(a+4) or 0=(a+2)$ $->$ there are two possible values for $a$

$a=-4 or a=-2$

How do you find the value of a given the points (a,2), (-3,3) with a distance of sqrt2sqrt2?