Question

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 $\sqrt{72}$ and the length of NL is $\sqrt{8}$. c. The slopes of LM and KN are both One-half and NK = ML = $\sqrt{20}$. d. The slope of KM is 1 and the slope of NL is –1.

Answer 1

Answer:

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 $(x_1,y_1)$ and $(x_2,y_2)$, then the rate of change is

$m=\frac{y_2-y_1}{x_2-x_1}$

Slope of KM is

$m_1=\frac{1-7}{1-7}=1$

Slope of LN is

$m_2=\frac{5-3}{3-5}=-1$

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

Find the product of slopes.

$m_1\cdot m_2=1\cdot (-1)=-1$

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.

Answer 2

Answer:

the answer is d on e2020

Step-by-step explanation: