Verify that the vertices A(-6.1),B(2,-5),C(6,1) and D(2,4) are the vertices of a trapezoid. Does anyone know the steps to solve this? Thanks so much.
slope ab = -6/8 = -3/4
slope bc = 6/4 = 3/2
slope cd = 3/-4 = -3/4
slope da = -3/8
note AB is parallel to CD
thanks so much?
could you please tell me the formulas you used to get those answers?
thanks so much!
could you please tell me the formulas you used to get those answers?
To verify if the given points A(-6, 1), B(2, -5), C(6, 1), and D(2, 4) form the vertices of a trapezoid, we can use the property that a quadrilateral is a trapezoid if it has one pair of parallel sides.
The formula to find the slope of a line passing through two points (x1, y1) and (x2, y2) is given by:
slope = (y2 - y1) / (x2 - x1)
Let's calculate the slopes of the opposite sides of the quadrilateral:
1. Slope of AB:
mAB = (-5 - 1) / (2 - (-6)) = (-6) / (8) = -3 / 4
2. Slope of CD:
mCD = (4 - 1) / (2 - 6) = (3) / (-4) = -3 / 4
Now, if the slopes of AB and CD are equal, then sides AB and CD are parallel, implying the given points form a trapezoid.
In this case, the slopes of AB and CD are both -3/4, which means AB and CD are parallel. Therefore, the given points A(-6, 1), B(2, -5), C(6, 1), and D(2, 4) indeed form the vertices of a trapezoid.
Remember, to verify if a quadrilateral is a trapezoid, calculate the slopes of opposite sides and check if they are equal.