Given the set of points as vertices of quadrilateral QRST, determine whether it is a rhombus, a rectangle, or a square. Choose all that apply.Q(1, 2), R(–2, –1), S(1, –4), T(4, –1)Question 6Select one or more:a.None of these b.Rectanglec.Kited.rhombuse.square

To determine the type of quadrilateral, we need to calculate the distances between the points.

1. Calculate the distance between Q and R, Q and T, R and S, and S and T. If all four distances are equal, then it is a rhombus.

2. Calculate the distance between Q and S, and R and T. If these distances are equal, then it is a rectangle.

3. If both conditions are met, then it is a square.

Let's calculate:

1. Distance between Q and R = sqrt[(1 - (-2))^2 + (2 - (-1))^2] = sqrt[9 + 9] = sqrt[18]
2. Distance between Q and T = sqrt[(1 - 4)^2 + (2 - (-1))^2] = sqrt[9 + 9] = sqrt[18]
3. Distance between R and S = sqrt[(-2 - 1)^2 + (-1 - (-4))^2] = sqrt[9 + 9] = sqrt[18]
4. Distance between S and T = sqrt[(1 - 4)^2 + (-4 - (-1))^2] = sqrt[9 + 9] = sqrt[18]

Since all four sides are equal, it is a rhombus.

Now, let's calculate the diagonals:

1. Distance between Q and S = sqrt[(1 - 1)^2 + (2 - (-4))^2] = sqrt[0 + 36] = sqrt[36] = 6
2. Distance between R and T = sqrt[(-2 - 4)^2 + (-1 - (-1))^2] = sqrt[36 + 0] = sqrt[36] = 6

Since the diagonals are equal, it is a rectangle.

Therefore, the given quadrilateral is a square. So, the correct answer is e. square.