How do you find the value of a given the points (6,-7), (a,-4) with a distance of #sqrt18#?

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Answer 1 · 2016-07-24T16:19:54

#a=3# or #a = 9#

Calling #p_1={6,-7}# and #p_2={a,-4}# the distance #d# between
#p_1# and #p_2# is obtained using Pitagoras.

#d = sqrt((6-a)^2+(-7+4)^2) = sqrt(18)#

Squaring both sides

#(6-a)^2+(-7+4)^2=18#

developing results

#a^2-12a+27=0#

Solving for #a# we obtain two solutions

#a=3# and #a = 9#