A quadrilateral with vertices K(0,4), A(3,6), T(6,2) and E(0,-2) is a ________.Question 12Select one:a.kiteb.trapezoidc.parallelogramd.square

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

1. Calculate the distance between K and A, A and T, T and E, and E and K. This will give us the lengths of the sides of the quadrilateral.
2. Calculate the distance between K and T, and A and E. This will give us the lengths of the diagonals of the quadrilateral.

The formula to calculate the distance between two points (x1, y1) and (x2, y2) is sqrt((x2-x1)^2 + (y2-y1)^2).

1. KA = sqrt((3-0)^2 + (6-4)^2) = sqrt(9+4) = sqrt(13)
2. AT = sqrt((6-3)^2 + (2-6)^2) = sqrt(9+16) = sqrt(25) = 5
3. TE = sqrt((0-6)^2 + (-2-2)^2) = sqrt(36+16) = sqrt(52)
4. EK = sqrt((0-0)^2 + (-2-4)^2) = sqrt(0+36) = sqrt(36) = 6
5. KT = sqrt((6-0)^2 + (2-4)^2) = sqrt(36+4) = sqrt(40)
6. AE = sqrt((0-3)^2 + (-2-6)^2) = sqrt(9+64) = sqrt(73)

We have KA = sqrt(13), AT = 5, TE = sqrt(52), EK = 6, KT = sqrt(40), and AE = sqrt(73).

From these lengths, we can see that opposite sides are not equal (KA ≠ TE and AT ≠ EK), so the quadrilateral is not a parallelogram or a square. The diagonals are also not equal (KT ≠ AE), so the quadrilateral is not a kite.

However, one pair of opposite sides are parallel (KA is parallel to TE because their slopes are equal), so the quadrilateral is a trapezoid.

So, the answer is b. trapezoid.