Answer:
The shape formed is a quadrilateral.
Explanation:
The four points A(-1,0), B(0,2), C(4,0), and D(3,-2) can be used to form a quadrilateral. To identify the shape formed by these points, we can use the distance formula to find the length of each side of the quadrilateral, and then compare the side lengths.
AB: Distance between A(-1,0) and B(0,2)
= sqrt((0 - (-1))^2 + (2 - 0)^2)
= sqrt(1 + 4)
= sqrt(5)
BC: Distance between B(0,2) and C(4,0)
= sqrt((4 - 0)^2 + (0 - 2)^2)
= sqrt(16 + 4)
= sqrt(20)
= 2 sqrt(5)
CD: Distance between C(4,0) and D(3,-2)
= sqrt((3 - 4)^2 + (-2 - 0)^2)
= sqrt(1 + 4)
= sqrt(5)
DA: Distance between D(3,-2) and A(-1,0)
= sqrt((-1 - 3)^2 + (0 - (-2))^2)
= sqrt(16 + 4)
= 2 sqrt(5)
Since the length of AB is not equal to the length of CD, and the length of BC is not equal to the length of DA, we can conclude that the quadrilateral formed by these four points is not a parallelogram or a rhombus. Additionally, since the length of AB is not equal to the length of CD, we can conclude that the quadrilateral is not a kite.
By comparing the angles formed by the line segments AB, BC, CD, and DA, we can see that the angle at B is a right angle, while the other three angles are all acute angles. This indicates that the quadrilateral is a trapezoid. Specifically, it is a right trapezoid, since it has one right angle.