Question

If the distance between the points (3, x) and (–2, –6) is 13 units, then find the value of x.

Answer 1

Given: Points (3, x) and (–2, –6), distance = 13.

Step-wise calculation:

1. Use the distance formula:

Distance = `sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2`

2. `sqrt((3 - (-2))^2 + (x - (-6))^2) = 13`

3. `sqrt(5^2 + (x + 6)^2) = 13`

4. Square both sides: 25 + (x + 6)² = 169

5. (x + 6)² = 144

6. x + 6 = ±12

⇒ x = 6 or x = –18