Question

The points ????(0,0), ????(−4,1), ????(−3,5), and ????(1,4) are the vertices of parallelogram OABC Is this parallelogram a

rectangle? Support your answer.

Answer 1

Yes, parallelogram OABC is a rectangle.

Step-by-step explanation:

The vertices of a parallelogram are O(0,0), A(-4,1), B(-3,5) and C(1,4).

A parallelogram is a rectangle if its any two adjacent sides are perpendicular to each other.

product of slopes of two perpendicular lines is -1.

Formula for slope is

`Slope=(y_2-y_1)/(x_2-x_1)`

Using the formula we get

`m_(OA)=(1-0)/(-4-0)=-(1)/(4)`

`m_(AB)=(5-1)/(-3-(-4))=-(4)/(1)=4`

`m_(OA)* m_(AB)=-(1)/(4)* 4=-1`

It means OA is perpendicular to AB.

Since two adjacent sides are perpendicular, therefore the given parallelogram OABC is a rectangle.