Find the distance between the points (\(\frac{1}{2}\), \(\frac{1}{2}\)) and (-\(\frac{1}{2}\), -\(\frac{1}{2}\)).
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Correct Answer: Option D
Explanation:
Let D denote the distance between (\(\frac{1}{2}\), -\(\frac{1}{2}\)) then using
D = \(\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\)
= \(\sqrt{(-{\frac{1}{2} - \frac{1}{2}})^2 + (-{\frac{1}{2} - \frac{1}{2}})^2}\)
= \(\sqrt{(-1)^2 + (-1)^2}\)
= \(\sqrt{1 + 1}\)
= √2
Let D denote the distance between (\(\frac{1}{2}\), -\(\frac{1}{2}\)) then using
D = \(\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\)
= \(\sqrt{(-{\frac{1}{2} - \frac{1}{2}})^2 + (-{\frac{1}{2} - \frac{1}{2}})^2}\)
= \(\sqrt{(-1)^2 + (-1)^2}\)
= \(\sqrt{1 + 1}\)
= √2