Answer: The answer is (D). No, the adjacent sides are not perpendicular.
Step-by-step explanation: We are given a shape on the co-ordinate plane and we are to check the correct statement about the shape from the given options.
The shape has four vertices A(4, -1), B(2, 4), C(-2, 2) and D(0, -3). So, the shape is definitely a quadrilateral. We are to check whether it is a rectangle or not.
We will find the slope of all the sides AB(m), BC(n), CD(o) and DA(p) as follows:
[tex]m=\dfrac{4+1}{2-4}=-\dfrac{5}{2},\\\\n=\dfrac{2-4}{-2-2}=\dfrac{1}{2},\\\\o=\dfrac{-3-2}{0+2}=-\dfrac{5}{2},\\\\p=\dfrac{-3+1}{0-4}=\dfrac{1}{2}.[/tex]
Since,
[tex]m=o,~~n=p,[/tex]
so the opposite sides are parallel, but
[tex]m\times n\neq -1,~~n\times o\neq -1,~~o\times p\neq -1,~~p\times m\neq -1,[/tex]
so the adjacent sides are not perpendicular.
Thus, (D) is the correct option.
