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Igoryamba
2 years ago
5

If the distance between A(0, 4) and B(3,a) is 5 units then find the value of a.​

Mathematics
2 answers:
Anna007 [38]2 years ago
4 0

Answer:

Step-by-step explanation:

a = 0

So that AOB makes a right triangle with sides 3-4-5

Phoenix [80]2 years ago
4 0

Answer:

a = 8

Step-by-step explanation:

Calculate AB using the distance formula and equate to 5

d = \sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2    }

with (x₁, y₁ ) = A (0, 4 ) and (x₂, y₂ ) = B (3, a )

d = \sqrt{(3-0)^2+(a-4)^2}

  = \sqrt{3^2+(a-4)^2}

  = \sqrt{9+(a-4)^2} , then

\sqrt{9+(a-4)^2} = 5 ( square both sides )

9 + (a - 4)² = 5² = 25 ( subtract 9 from both sides )

(a - 4)² = 16 ( take square root of both sides )

a - 4 = 4 ( add 4 to both sides )

a = 8

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