Question

draw the polygon whose vertices are (-1, 0), (4, 3), (4, -3), and (-1, -2). then choose the best description of the polygon from the choices below. square trapezoid triangle none of these

Explanation:

Step1: Recall the properties of polygons

We know the properties of square (all - sides equal and all - angles 90°), trapezoid (one pair of parallel sides), and triangle (3 sides).

Step2: Analyze the given vertices

The vertices are \(A(-1,0)\), \(B(4,3)\), \(C(4, - 3)\), \(D(-1,-2)\). The \(x\) - coordinate of \(B\) and \(C\) is \(4\), so the line segment \(BC\) is a vertical line. The \(x\) - coordinate of \(A\) and \(D\) is \(-1\), so the line segment \(AD\) is a vertical line. The length of \(BC=3-( - 3)=6\), the length of \(AD = 0-( - 2)=2\). The length of the non - vertical sides can be found using the distance formula \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\). The distance between \(A(-1,0)\) and \(B(4,3)\) is \(d_{AB}=\sqrt{(4 + 1)^2+(3 - 0)^2}=\sqrt{25 + 9}=\sqrt{34}\), and the distance between \(D(-1,-2)\) and \(C(4,-3)\) is \(d_{DC}=\sqrt{(4 + 1)^2+(-3 + 2)^2}=\sqrt{25+1}=\sqrt{26}\). Since one pair of sides (\(AD\) and \(BC\)) is parallel and the other two sides are non - parallel and non - equal in length, it is a trapezoid.

Answer:

Trapezoid