Find the value of t, if the distance between the points P(-3, -14) and Q(t, -5) is 9 units.

Step 1: Write distance formula
Distance = √[(x₂ – x₁)² + (y₂ – y₁)²]
P(-3, -14) = (x₁, y₁)
Q(t, -5) = (x₂, y₂)

Step 2: Substitute values
9 = √[(t – (-3))² + (-5 – (-14))²]
9 = √[(t + 3)² + (9)²]
9 = √[(t + 3)² + 81]

Step 3: Square both sides
81 = (t + 3)² + 81

Step 4: Solve for t
81 – 81 = (t + 3)²
0 = (t + 3)²
0 = t + 3
t = -3

Step 5: Verify
Distance = √[(-3 + 3)² + (9)²]
= √[0 + 81]
= √81 = 9 ✓