How do you find a possible value for a if the points (4,a), (8,4) has a distance of #d=2sqrt5#?

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Answer 1 · 2017-04-27T07:15:23

a = 6 or 2

We know the distance between two points = #sqrt[(x_2-x_1)^2+(y_2-y_1)^2]# where #(x_1,y_1) = (4,a) and (x_2,y_2) = (8,4)#

Hence #sqrt[(8-4)^2+(4-a)] = 2sqrt5# [as per question]

or, #(8-4)^2+(4-a)^2 = [2 sqrt5]^2# [ squiring both sides]

#rArr 4^2+16-8a+a^2 = 20#

#rArr a^2 - 8a +16+16-20 = 0#

#rArr a^2 - 8a +12 = 0#

#rArr a^2-2a-6a+12 = 0#

#rArr a(a-2)-6(a-2)=0#

#rArr (a-6)(a-2)=0#

#rArr (a-6)=0, (a-2)=0#

#rArr a =6 or 2#