Which statement proves that parallelogram klmn is a rhombus?

a. the midpoint of both diagonals is (4, 4).
b. the length of km is √72 and the length of nl is √8.
c. the slopes of lm and kn are both 1/2 and nk = ml = √20 .
d. the slope of km is 1 and the slope of nl is –1.

D is  the right answer.The slope of KM is 1 and the slope of NL is –1.

Step-by-step explanation:

A rhombus is a parallelogram whose all sides are equal. Its diagonals perpendicularly bisect each other.

i.e. product of its slope should be -1.

[∵if one line is perpendicular to the other lines then product of its slope should be -1.]

In diagram

Slope of  KM=

Slope of NL=

Product of slope of diagonals=1×-1=-1

∴diagonals of given parallelogram perpendicularly bisect each other.

Therefore,it is a rhombus.

step-by-step explanation:

y = | -2(-2) |     →     y = | 4 |     →     y = 4       ⇒   (-2, 4)

y = | -2(-1) |     →     y = | 2 |     →       y =   2       ⇒   (-1, 2)    

y = | -2(0) |     →     y = | 0 |     →       y = 0         ⇒   (0, 0)

y = | -2(1) |   c →     y = | -2 |     →     y =   2         ⇒   (1, 2)    

y = | -2(2) |     →     y = | - 4 |     →     y =   4         ⇒   (2, 4)