Question

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

Answer 1

Explanation:

a = 0

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

Answer 2

a = 8

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 =
`√((3-0)^2+(a-4)^2)`

=
`√(3^2+(a-4)^2)`

=
`√(9+(a-4)^2)` , then

`√(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