Find the distance between the points ($\frac{1}{2}$, $\frac{1}{2}$) and (-$\frac{1}{2}$, -$\frac{1}{2}$).

Analyze the question: We need the distance between two points on a coordinate plane, so the distance formula applies.

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

d = √[(x₂ − x₁)² + (y₂ − y₁)²]

Solution:

Let (x₁, y₁) = (½, ½) and (x₂, y₂) = (−½, −½).

• x₂ − x₁ = −½ − ½ = −1
• y₂ − y₁ = −½ − ½ = −1

d = √[(−1)² + (−1)²] d = √(1 + 1) d = √2

Answer: The distance is √2, which matches option D.

(Option B, "o", is presumably meant to be 0, which would only be correct if the two points were the same. They are clearly different points.)

Tip: Squaring removes the negative signs, so don't worry about them. Also remember that the points (a, a) and (−a, −a) always lie on the line y = x, and the distance between them is 2a√2. Here a = ½, so d = 2(½)√2 = √2.