**Answer:**

Yes, it is a rhombus because the slope of diagonal segment BD equals 2, the slope of diagonal segment AC equals -1/2, and the diagonals bisect each other.

**Step-by-step explanation:**

The slope of diagonal BD is ...

slope BD = (change in y)/(change in x) = (-4/-2) = 2

The slope of diagonal AC is ...

slope AC = (change in y)/(change in x) = (4/-8) = -1/2

The midpoint of BD is ...

((-4, 5) +(-6, 1))/2 = (-10, 6)/2 = (-5, 3)

The midpoint of AC is ...

((-1, 1) +(-9, 5))/2 = (-10, 6)/2 = (-5, 3)

so the diagonals bisect each other.

While the third statement is true (both midpoints are the same), that fact alone is not sufficient to allow the figure to be declared a rhombus. The diagonals must also be perpendicular (have slopes whose product is -1). The appropriate answer choice is the **<em>second one</em>**:

**Yes, it is a rhombus because the slope of diagonal segment BD equals 2, the slope of diagonal segment AC equals -1/2, and the diagonals bisect each other.**