Verify the parallelogram with abcd with vertices. A(-5,-1), b(-9,6)
To verify that the quadrilateral ABCD with vertices A(-5,-1), B(-9,6), C(1,2), and D(5,-5) is a parallelogram, we need to show that the opposite sides are parallel.
First, let's find the slope of the line AB:
m = (y2 - y1) / (x2 - x1)
m = (6 - (-1)) / (-9 - (-5))
m = 7 / -4
m = -7/4
Next, let's find the slope of the line CD:
m = (y2 - y1) / (x2 - x1)
m = (-5 - 2) / (5 - 1)
m = -7 / 4
m = -7/4
Since the slopes of AB and CD are the same, AB and CD are parallel.
Now, let's find the slope of the line BC:
m = (y2 - y1) / (x2 - x1)
m = (2 - 6) / (1 - (-9))
m = -4 / 10
m = -2/5
Next, let's find the slope of the line AD:
m = (y2 - y1) / (x2 - x1)
m = (-5 - (-1)) / (5 - (-5))
m = -4 / 10
m = -2/5
Since the slopes of BC and AD are the same, BC and AD are parallel.
Therefore, all opposite sides of the quadrilateral ABCD with vertices A(-5,-1), B(-9,6), C(1,2), and D(5,-5) are parallel. Hence, ABCD is a parallelogram.