Question

The coordinates of the vertices of​ quadrilateral ABCD ​ are A(−4, −1) , B(−1, 2) , C(5, 1) , and D(1, −3) .

The slope of ​ AB ​ is ______ , the slope of ​ BC is _____, the slope of CD is_____ , and the slope of ​ AD is _____ . Quadrilateral ABCD is a parallelogram because.______

Answer 1

The slopes of the sides of quadrilateral ABCD are found using the slope formula, resulting in slopes of AB as 1, BC as -1/6, CD as 1, and AD as -2/5. Quadrilateral ABCD is a parallelogram because the opposite sides have equal slopes.

Step-by-step explanation:

The slopes of the sides of quadrilateral ABCD can be calculated using the formula for slope, which is = (y2 - y1) / (x2 - x1). For line AB, the coordinates are A(-4, -1) and B(-1, 2). Therefore, the slope of AB is (2 - (-1)) / (-1 - (-4)) = 3 / 3 = 1. For line BC, using points B(-1, 2) and C(5, 1), the slope of BC is (1 - 2) / (5 - (-1)) = -1 / 6. Moving on to line CD, with points C(5, 1) and D(1, -3), the slope of CD is (-3 - 1) / (1 - 5) = -4 / -4 = 1. Finally, for line AD with points A(-4, -1) and D(1, -3), the slope of AD is (-3 - (-1)) / (1 - (-4)) = -2 / 5. Quadrilateral ABCD is a parallelogram because the opposite sides have the same slope; slope of AB equals slope of CD, and slope of BC equals slope of AD.