A quadrilateral has vertices (0, -1), (6, 7), (-2, 3) and (8, 3). The quadrilateral is a:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → Rectangle
A quadrilateral whose diagonals are equal and bisect each other is a rectangle; it is a square only if its sides are also equal. Plotting the points shows that (0, −1) and (6, 7) are opposite corners, and so are (−2, 3) and (8, 3).
The diagonals:
(0, −1) to (6, 7): length \(=\sqrt{6^2+8^2}=10\), midpoint (3, 3)
(−2, 3) to (8, 3): length \(=10\), midpoint (3, 3)
Equal diagonals with the same midpoint: the figure is a rectangle
The sides (to tell a rectangle from a square):
(0, −1) to (8, 3): \(\sqrt{8^2+4^2}=\sqrt{80}\)
(8, 3) to (6, 7): \(\sqrt{2^2+4^2}=\sqrt{20}\)
Adjacent sides are unequal, so it is not a square (and not a rhombus)