What kind of quadrilateral do we get with the vertices (–4, 4), (–6, 0), (–4, –4), (–2, 0) by plotting it on a graph?

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Parallelogram

Rectangle

Square

Rhombus

answer is D.

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Detailed Solution

Let ABCD be a quadrilateral with the vertices A(–4, 4), B(–6, 0), C(–4, –4), D(–2, 0).
Draw these points on graph paper.
Join the coordinates.
Draw the quadrilateral with vertices left(-4,4right),left(-6,0right),(-4,-4) and (-2,0). Also name the type of quadrilateral and find its area. | Snapsolve

Draw the quadrilateral with vertices left(-4,4right),left(-6,0right),(-4,-4) and (-2,0). Also name the type of quadrilateral and find its area. | Snapsolve

Therefore from the figure, we have,

A B = B C = C D = D A

.
This shows that all the sides of the quadrilateral ABCD are equal but the sides are not perpendicular to each other as shown in the graph.
Therefore, the given quadrilateral ABCD is a rhombus.
Hence, option (4) is correct.

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