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#