Can someone help me out with this problem thanks will give brainliest

 The answer is (B) square because all four sides are congruent and adjacent sides are perpendicular.

Step-by-step explanation: We are given a quadrilateral ABCD with co-ordinates of the vertices A(3, 5), B(5, 2), C(8, 4) and D(6, 7).

We know that if (a, b) and (c,d) are any two points, then the distance between them is given by the formula:

The length of the sides AB, BC, CD and DA are calculated by the distance formula as follows:

Now, the slopes of all the sides are calculated as follows:

Therefore, we have

m × n = n × o = o × p = p × m = -1.

Hence, the adjacent sides are perpendicular, since the product of the slopes of two perpendicular lines is - 1.

Therefore, ABCD is a square, because all the sides are congruent and adjacent sides are perpendicular.

Thu, (B) is the correct option.