Question

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.

Answer 1

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

Explanation:

A rectangle has the following features:

• Opposite sides are equal
• Opposite side are parallel (same slope)
• all the interior angle are 90° (adjacent sides are perpendicular)

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