Correct option is (b) square
Let A(−1, −2), B(1, 0), C(−1, 2) and D(3, 0).
Distance between two points (x1, y1) and (x2, y2) can be calculated using the formula \(\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\)
Distance between the points A(−1,−2) and B (1,0) = \(\sqrt{(1 + 1)^2 + (0 + 2)^2}\)
\(= \sqrt{4 + 4}\)
\(= \sqrt 8\)
Distance between the points B(1, 0) and C (−1, 2) = \(\sqrt{(-1 - 1)^2 + (2-0)^2}\)
\(= \sqrt{4 + 4}\)
\(= \sqrt 8\)
Distance between the points C(−1, 2) and D (−3, 0) = \(\sqrt{(-3 + 1)^2 + (0 -2)^2}\)
\(= \sqrt{4 + 4}\)
\(= \sqrt 8\)
Distance between the points A(−1, −2) and D (−3, 0) = \(\sqrt{(-3 + 1)^2 + (0 +2)^2}\)
\(= \sqrt{4 + 4}\)
\(= \sqrt 8\)
Since, length of the sides between all vertices are equal, they are the vertices of a square.
