Final answer:
The line y=1/2(x) does intersect the unit circle at two points because after substituting the equation of the line into the unit circle equation, we find real number solutions for x.
Step-by-step explanation:
To determine if the line y=1/2(x) intersects the unit circle, which is defined by the equation x^2 + y^2 = 1, we can substitute the expression for y from the line's equation into the equation of the unit circle and solve for x. Substituting y gives us: x^2 + (1/2x)^2 = 1.
We simplify that to: x^2 + 1/4x^2 = 1, which further simplifies to 5/4x^2 = 1. After multiplying both sides by 4/5 to solve for x^2, we get x^2 = 4/5. Now, take the square root of both sides: x = +-sqrt(4/5), which provides two real numbers for x. Since these solutions yield real numbers, it indicates that there are two points where the line intersects the unit circle, hence the answer is (b) Yes.