Alg6.6

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Find the value of a if the distance between the points (a,2),(3,4)\, is 2.

The distance between the given points is

{\sqrt  {(a-3)^{2}+(2-4)^{2}}}=2\,

Simplifying

{\sqrt  {a^{2}+9-6a+4}}=2\,

Squaring on both sides,

a^{2}-6a+13=4\,

a^{2}-6a+9=0\,

(a-3)^{2}=0\,

Hence the value of a is 3.

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