Question

quadrilateral abcd is graphed on the set of axes below. what is the most precise name for the quadrilateral? parallelogram rhombus rectangle square

Explanation:

Step1: Recall properties of quadrilaterals

A parallelogram has opposite sides parallel. A rhombus is a parallelogram with all sides equal. A rectangle is a parallelogram with right - angles. A square is a rhombus and a rectangle (all sides equal and right - angles).

Step2: Analyze the given quadrilateral

From the graph (by counting units or using distance formula \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\)), we can find that the adjacent sides are equal in length. Also, there is no indication of right - angles (by checking slopes of adjacent sides, if \(m_1\times m_2=- 1\) for perpendicular lines). The opposite sides are parallel (by checking slopes of opposite sides, if \(m_1 = m_2\) for parallel lines). Since all sides are equal and it is a parallelogram (opposite sides parallel), it is a rhombus.

Answer:

rhombus