Which of the following information would prove the quadrilateral ABCD is a rectangle? Question 2 options:

a) The length of segment AB and CD is 5 units and length of segment BC and DA is 12

b) Slope of AB = 2, Slope of BC = -1/2, Slope of CD = 2, and slope of of DA = -1/2

c) Slope of AB = 2, Slope of BC = -3/2, Slope of CD = 2, and slope of of DA = -3/2

d) Slope of AB = 2, slope of CD = 2, and the length of segment AB and CD is 5.

The correct option is B

B) Slope of AB = 2, Slope of BC = -1/2, Slope of CD = 2, and slope of of DA = -1/2

Step-by-step explanation:

A rectangle has the following features:

Considering these point, the best options is B because:

AB || CD = opposite sides have same slope 2 (they are parallel)

BC || DA = opposite sides have same slope -1/2 (they are parallel)

For 2 lines to be perpendicular:

Slope of line 1 = -1/ (Slope of line 2)

Let line 1 be AB and line 2 be BC

Slope of AB = -1/(Slope of BC)

2 = -1/(-1/2 )

2=2

Hence proved

As two points are true, third point will also be true

x= -3 and

step-by-step explanation:

to find the roots of a cubic, use division or factoring to find the factors then set equal to 0. as this is a difference of cubes, it factors into

where a is the cube root of .

here   this is 27 and the cube root of 27 is 3. so we write using the form:

.

set each factor to 0 and solve for x.

x-3=0

x=3

the quadratic expression does not factor and must be solved using the quadratic formula.

where a = 1, b=3, and c=9

this cubic has two complex roots.