Three vertices of the trapezoid are A(4d, 4e), B(4f, 4e), and C(4g, 0). The fourth vertex lies on the origin. Find the midpoint of the midsegment of the trapezoid.
A trapezoid is graphed in the first quadrant of the coordinate plane with no grid. The lower left vertex is the origin. Point A is up and right from the origin. Point B is right of point A. Point C is on the x-axis below and right of point B.
(1 point)
Responses
(2f, 2e)
(2 f , 2 e )
(d + f + g, e)
( d + f + g , e )
(d + f + g, 2e)
( d + f + g , 2 e )
(2d + 2g, 2e)
The midsegment of a trapezoid is parallel to the bases of the trapezoid and its length is equal to the average of the lengths of the bases.
The length of the base AD is 4f - 4d = 4(f - d).
The length of the base BC is 4g - 4f = 4(g - f).
The length of the midsegment is the average of the lengths of the bases:
(4(f - d) + 4(g - f))/2 = 2(g - d).
Since the midpoint of the midsegment is halfway between the endpoints, the x-coordinate of the midpoint is (4d + 4g)/2 = 2(d + g), and the y-coordinate of the midpoint is (4e + 0)/2 = 2e.
Therefore, the midpoint of the midsegment is (2(d + g), 2e).
Answer: (d + g , e).