Answer:
b. parallelogram
Explanation:
The figure cannot be square because a square has four congruent sides and four right angles, and this figure does not have either of those properties.
The figure cannot be a triangle because a triangle has only three vertices, and this figure has four vertices.
The figure cannot be a trapezoid because a trapezoid has at least one pair of parallel sides, and it is not clear from the given information whether any of the sides are parallel.
The figure could be a parallelogram, which is a quadrilateral with opposite sides parallel. To determine whether this is the case, we can check whether the slopes of opposite sides are equal. Here are the slopes of the sides:
AB: (4-1)/(1-(-4)) = 3/5
BC: (-1-4)/(6-1) = -5/5 = -1
CD: (-4-(-1))/(1-6) = 3/5
DA: (1-(-4))/(-4-1) = -5/5 = -1
We can see that the slopes of opposite sides AB and CD are equal, and the slopes of opposite sides BC and DA are equal. Therefore, the figure is a parallelogram.
The figure cannot be a kite because a kite is a quadrilateral with two pairs of adjacent congruent sides, and this figure does not have that property.
So the answer is: b. parallelogram.