Question

Find the value(s) of x, if the distance between the points A(0, 0) and B(x, –4) is 5 units.

Answer 1

Given: A(0, 0), B(x, –4), distance AB = 5.

Step-wise calculation:

1. Distance formula:

`AB = sqrt((x - 0)^2 + (-4 - 0)^2)` 

= `sqrt(x^2 + 16)`

2. Set equal to 5:

`sqrt(x^2 + 16) = 5`

3. Square both sides:

x² + 16 = 25

4. Solve:

x² = 9

⇒ x = ±3

Verify: For x = 3 or –3, 

`sqrt(9 + 16) = sqrt(25)` 

= 5