On a coordinate plane, parallelogram k l m n shown. point k is at (7, 7), point l is at (5, 3), point m is at (1, 1), and point n is at (3, 5). which statement proves that parallelogram klmn is a rhombus? a. the midpoint of both diagonals is (4, 4). b. the length of km is and the length of nl is . c. the slopes of lm and kn are both one-half and nk = ml = . d. the slope of km is 1 and the slope of nl is –1.

Option D.

Step-by-step explanation:

Given information: KLMN is parallelogram, K(7,7), L(5,3), M(1,1) and N(3,5).

Diagonals of a parallelogram bisect each other.

If diagonals of a parallelogram are perpendicular to each other then the parallelogram is a rhombus.

If a line passes through two points and , then the rate of change is

Slope of KM is

Slope of LN is

The product of slopes of two perpendicular lines is -1.

Find the product of slopes.

The product of slopes of KM and NL is -1. It means diagonals are perpendicular and KLMN is a rhombus.

Therefore, the correct option is D.