Question

Decide whether quadrilateral ABCD with vertices 4(-3,0), B(-4,1), C(-1.4), and D(0,3) is a rectangle, rhombus, square, or parallelogram.

Answer 1

Answer: rectangle

Explanation:

The options imply the figure is a parallelogram. Furthermore, we can tell that not all the sides are congruent, so we can rule out the possibility that it is a rhombus or a square.

To determine if it is a rectangle, we can use the slope formula to determine if there is a pair of perpendicular sides. If this is the case, then this will be a parallelogram with a right angle, making it a rectangle.

`m_{\overline{AB}}=(1-0)/(-4-(-3))=-1\\m_{\overline{BC}}=(4-1)/(-1-(-4))=1\\\therefore \overline{AB} \perp \overline{BC}`

So, the most specific classification is a rectangle