Trapezoid RSTU has vertices R(−3,0), S(0,−1), T(2,5), and U(−7,8).
Part A:
Determine the slope for each side of the trapezoid.
Part B:
Based on the results to Part A, which sides of the trapezoid are parallel? Explain your reasoning.
To find the slope of a line, we can use the formula:
slope (m) = (y2 - y1) / (x2 - x1)
Using this formula, we can find the slope for each side of the trapezoid:
Side RS:
slope (m) = (-1 - 0) / (0 - (-3)) = -1 / 3
Side ST:
slope (m) = (5 - (-1)) / (2 - 0) = 6 / 2 = 3
Side TU:
slope (m) = (8 - 5) / (-7 - 2) = 3 / -9 = -1/3
Side UR:
slope (m) = (0 - 8) / (-3 - (-7)) = -8 / 4 = -2
Based on the results from Part A, we can see that side RS and side TU have the same slope (-1/3), while side ST and side UR have the same slope (3).
The sides RS and TU are parallel because they have the same slope. Similarly, the sides ST and UR are parallel because they have the same slope.
This is based on the property of trapezoids, where the non-parallel sides are called the legs and have different slopes, while the parallel sides are called the bases and have the same slope.