A (2, 4), B (2, 8), C (6, 8), D (6, 4) are the points in first quadrant. If AB, BC, CD and DA joined then □ABCD is
A (2, 4), B (2, 8), C (6, 8), D (6, 4) are the points in first quadrant. If AB, BC, CD and DA joined then □ABCD is
A) Rectangle
B) Trapezium
C) Parallelogram
D) Square
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2 Answers
Correct option is (D) Square
AB = \(\sqrt{(2-2)^2+(8-4)^2}\) = 4 units
BC = \(\sqrt{(6-2)^2+(8-8)^2}\) = 4 units
CD = \(\sqrt{(6-6)^2+(4-8)^2}\) = 4 units
DA = \(\sqrt{(2-6)^2+(4-4)^2}\) = 4 units
AC = \(\sqrt{(6-2)^2+(8-4)^2}\) = \(\sqrt{16+16}\) = \(4\sqrt2\) units
BD = \(\sqrt{(6-2)^2+(4-8)^2}\) = \(\sqrt{16+16}\) = \(4\sqrt2\) units
Since, AB = BC = CD = DA and AC = BD
\(\therefore\) ABCD is a square.
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