JAMB Mathematics 2010 Paper

Concept:The distance between two coordinate points is the length of the straight line joining them, calculated using Pythagoras' theorem.Explanation:Let $(x_1, y_1) = \left(\frac{1}{2}, \frac{1}{2}\right)$ and $(x_2, y_2) = \left(-\frac{1}{2}, -\frac{1}{2}\right)$.Apply the distance formula: $D = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$.First, find the change in $x$: $x_2 - x_1 = -\frac{1}{2} - \frac{1}{2} = -1$.Then, find the change in $y$: $y_2 - y_1 = -\frac{1}{2} - \frac{1}{2} = -1$.Substitute these differences into the formula: $D = \sqrt{(-1)^2 + (-1)^2}$.Square each term: $(-1)^2 = 1$ and $(-1)^2 = 1$.Add the squares: $D = \sqrt{1 + 1} = \sqrt{2}$.Therefore, the points are $\sqrt{2}$ units apart.Answer:$D = \sqrt{2}$, so the correct option is D.