Question

The points $(-2,1),(0,3),(2,1)$ and $(0,-1)$ are the vertices of a ________.

• A. parallelogram.
• B. scalene quadrilateral
• C. isosceles quadrilateral
• D. concave quadrilateral

Answer 1

The correct option is A parallelogram.

If the points are $P(x_1,y_1)$ and $Q(x_2,y_2)$, the slope of the line joining PQ is $\frac{y_2-y_2}{x_2-x_1}$

For points, $A(-2,1),B(0,3),C(2,1)$ and $D(0,-1)$,
Slope of $AB=\frac{3-1}{0+2}=1$

Slope of $BC=\frac{1-3}{2-0}=-1$

Slope of $CD=\frac{-1-1}{0-2}=1$
Slope of $DA=\frac{-1-1}{0+2}=-1$

Clearly slope of $AB=$ Slope of $CD$, hence, $AB\parallel CD$.
Clearly slope of $BC=$ Slope of $DA$, hence, $BC\parallel DA$.

Since, the set of opposite sides are parallel to each other.

Thus, $\square ABCD$ are the vertices of a parallelogram.