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
[tex]Slope=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
Using the formula we get
[tex]m_{OA}=\dfrac{1-0}{-4-0}=-\dfrac{1}{4}[/tex]
[tex]m_{AB}=\dfrac{5-1}{-3-(-4)}=-\dfrac{4}{1}=4[/tex]
[tex]m_{OA}\times m_{AB}=-\dfrac{1}{4}\times 4=-1[/tex]
It means OA is perpendicular to AB.
Since two adjacent sides are perpendicular, therefore the given parallelogram OABC is a rectangle.
