LM¯¯¯¯¯¯¯¯¯ is the midsegment of trapezoid ABCD. If AB =50 and DC = 135, what is LM? Please show all work in order to recieve full credit for this problem
A trapezoid is a quadrilateral with one pair of parallel sides. In a trapezoid, the midsegment is a line segment that connects the midpoints of the non-parallel sides.
In this case, AB and DC are the non-parallel sides of trapezoid ABCD, so LM is the midsegment that connects the midpoints of AB and DC.
To find LM, we need to find the lengths of AB and DC.
Given that AB = 50 and DC = 135, we can start by finding the midpoint of AB and the midpoint of DC.
The midpoint of a line segment with endpoints (x1, y1) and (x2, y2) can be found using the midpoint formula:
Midpoint = [(x1 + x2)/2 , (y1 + y2)/2]
For AB, the endpoints are A and B, which have coordinates (x1, y1) = (0, 0) and (x2, y2) = (50, 0) respectively.
Midpoint of AB = [(0 + 50)/2 , (0 + 0)/2] = [25, 0]
For DC, the endpoints are D and C, which have coordinates (x1, y1) = (0, 0) and (x2, y2) = (135, 0) respectively.
Midpoint of DC = [(0 + 135)/2 , (0 + 0)/2] = [67.5, 0]
Now that we have the coordinates of the midpoints, we can find the distance between them using the distance formula:
Distance = √[(x2 - x1)^2 + (y2 - y1)^2]
Distance = √[(67.5 - 25)^2 + (0 - 0)^2]
Distance = √[42.5^2 + 0] = √[1806.25] = 42.5
Therefore, LM = 42.5.