Question

Is the following shape a rectangle? How do you know?

Answer 1

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:

$m=\dfrac{4+1}{2-4}=-\dfrac{5}{2},\\\\n=\dfrac{2-4}{-2-2}=\dfrac{1}{2},\\\\o=\dfrac{-3-2}{0+2}=-\dfrac{5}{2},\\\\p=\dfrac{-3+1}{0-4}=\dfrac{1}{2}.$

Since,

$m=o,~~n=p,$

so the opposite sides are parallel, but

$m\times n\neq -1,~~n\times o\neq -1,~~o\times p\neq -1,~~p\times m\neq -1,$

so the adjacent sides are not perpendicular.

Thus, (D) is the correct option.

Answer 2

The answer is C. No, the adjacent sides are not perpendicular. (Apex)