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Question: The points A(–4,­–1), B (–2,–4), C(4,0) and D(2,3) are the vertices of....

The points A(–4,­–1), B (–2,–4), C(4,0) and D(2,3) are the vertices of.

A

Parallelogram

B

Rectangle

C

Rhombus

D

None of these

Answer

Rectangle

Explanation

Solution

Mid-points of diagonals are same.

Also SAB=−4+1−2+4=−32,SAD=3+12+4=23S _ { A B } = \frac { - 4 + 1 } { - 2 + 4 } = \frac { - 3 } { 2 } , S _ { A D } = \frac { 3 + 1 } { 2 + 4 } = \frac { 2 } { 3 }

SAB⋅SAD=−1S _ { A B } \cdot S _ { A D } = - 1 Hence it is a rectangle.