Question

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

Answer 1

Answer:

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

$Slope=\dfrac{y_2-y_1}{x_2-x_1}$

Using the formula we get

$m_{OA}=\dfrac{1-0}{-4-0}=-\dfrac{1}{4}$

$m_{AB}=\dfrac{5-1}{-3-(-4)}=-\dfrac{4}{1}=4$

$m_{OA}\times m_{AB}=-\dfrac{1}{4}\times 4=-1$

It means OA is perpendicular to AB.

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