Answer:
D.
Explanation:
The representation of this problem is shown below. To find the answer, we need to use the distance formula:

- The first diagonal is formed by the points A and C
- The second diagonal is formed by the points B and D
So, for the first diagonal:
![A(x_(1),y_(1))=A(-1,10) \\ \\ C(x_(2),y_(2))=C(1,8) \\ \\ \\ d_(1)=\sqrt{(x_(2)-x_(1))^2+(y_(2)-y_(1))^2} \\ \\ d_(1)=√([1-(-1)]^2+(8-10)^2)=2√(2)](https://img.qammunity.org/2020/formulas/mathematics/high-school/qml4vpgqn7fjat6743oxwmvfvoet3qql14.png)
For the second diagonal:
![B(x_(1),y_(1))=B(-4,5) \\ \\ D(x_(2),y_(2))=D(4,3) \\ \\ \\ d_(2)=\sqrt{(x_(2)-x_(1))^2+(y_(2)-y_(1))^2} \\ \\ d_(2)=√([4-(-4)]^2+(3-5)^2)=2√(17)](https://img.qammunity.org/2020/formulas/mathematics/high-school/oklsz7nh3k96nyecp97tpuqxfa36iyvioy.png)
So the diagonals aren't congruent. Are they perpendicular?

These two vectors will be perpendicular (hence the diagonals will be perpendicular) if and only if the dot product equals zero, so:

Thus, the diagonals aren't perpendicular. In conclusion:
D. The diagonals are neither congruent nor perpendicular, which means the quadrilateral is a parallelogram only.