Question

Find the value of \( x \) for which the distance between the points \( P(x, 4) \) and \( Q(9,10) \) is 10 units.

Hint:

Use the distance formula \( d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \).

Answer 1

Using distance formula:
\[ \sqrt{(x - 9)^2 + (4 - 10)^2} = 10. \] \[ \sqrt{(x - 9)^2 + 36} = 10. \] Squaring both sides:
\[ (x - 9)^2 + 36 = 100. \] \[ (x - 9)^2 = 64. \] \[ x - 9 = \pm 8. \] \[ x = 17 \text{ or } x = 1. \]