The coordinates of points P and Q are (4, 3) and (2, -1) respectively. Find the shortest distance between P and Q.

Analyze the question: The shortest distance between two points is the straight-line distance, so we use the distance formula.

Concept: For points (x₁, y₁) and (x₂, y₂):

d = √[(x₂ − x₁)² + (y₂ − y₁)²]

Solution:

P(4, 3) and Q(2, −1)

• x₂ − x₁ = 2 − 4 = −2
• y₂ − y₁ = −1 − 3 = −4

d = √[(−2)² + (−4)²] d = √(4 + 16) d = √20 d = √(4 × 5) d = 2√5

Answer: 2√5, which is option D.

Tip: When you get a square root, always check for a perfect-square factor (4, 9, 16, 25...). Here √20 = √4 × √5 = 2√5. Also, squaring removes negative signs, so don't worry about the order of subtraction.