Answer:
Since the slopes of both lines BE and ST are equal, we can conclude that the quadrilateral with vertices B(–4, 3), E(6, 5), S(7, –1), and T(–3, –3) is a parallelogram.
Step-by-step explanation:
To determine if the quadrilateral with vertices B(–4, 3), E(6, 5), S(7, –1), and T(–3, –3) is a parallelogram, we can use the slope of its sides.
The slope of line BE is calculated as follows: m<sub>BE</sub> = (y<sub>2</sub> - y<sub>1</sub>) / (x<sub>2</sub> - x<sub>1</sub>) = (5 - 3) / (6 - (-4)) = 2 / 10 = 1/5
The slope of line ST is calculated as follows: m<sub>ST</sub> = (y<sub>2</sub> - y<sub>1</sub>) / (x<sub>2</sub> - x<sub>1</sub>) = (-3 - (-1)) / (-3 - 7) = -2 / (-10) = 1/5
Since the slopes of both lines BE and ST are equal, we can conclude that the quadrilateral with vertices B(–4, 3), E(6, 5), S(7, –1), and T(–3, –3) is a parallelogram.