Question

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

Answer 1

Answer:

Step-by-step explanation:

a = 0

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

Answer 2

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