find the value of “a” if the distance between the points (a,2), (3,4) is 2√2

Question

find the value of “a” if the distance between the points (a,2), (3,4) is 2√2

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Natalia 4 weeks 2021-08-18T17:48:01+00:00 1 Answer 0 views 0

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    2021-08-18T17:49:12+00:00

    Answer:

    a =1 or a=5

    Step-by-step explanation:

    we can solve this by using the distance between the two points equation,

    √(3-a)^2 + (4-2)^2 =2√2

    squaring on both sides

    (3-a)^{2} +4=8

    9+a^{2} -6a +4 = 8 (Since (a-b)^{2} = a^{2}+b^{2} -2ab)\\a^{2}-6a+13=8\\a^{2}-6a =-5\\a^{2}-6a+5=0\\a^{2}-5a-a+5=0\\a(a-5)-1(a-5)=0\\(a-1)(a-5)=0\\a-1=0 or a-5=0\\a=1 ora=5

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