Question

Given trapezoid ABCD with coordinates A(-2,0), B(0,4), C(4,4), D(6,0), find the coordinates E and F which make up the midsegment of the trapezoid.

Answer 1

To find the midsegment of trapezoid ABCD, we determine the midpoints of the non-parallel sides, AD and BC, resulting in points E(2, 0) and F(2, 4), forming the midsegment EF.

Step-by-step explanation:

The midsegment of a trapezoid is a line segment that connects the midpoints of the non-parallel sides. To find points E and F, which make up the midsegment of trapezoid ABCD, we need to find the midpoints of segments AD and BC.

First, we find the midpoint of AD by averaging the x-coordinates and the y-coordinates of points A(-2,0) and D(6,0):

• The midpoint of AD is at E( ( -2 + 6 ) / 2, ( 0 + 0 ) / 2 ) = E(2, 0).

Next, we find the midpoint of BC by averaging the x-coordinates and the y-coordinates of points B(0,4) and C(4,4):

• The midpoint of BC is at F( ( 0 + 4 ) / 2, ( 4 + 4 ) / 2 ) = F(2, 4).

The midsegment of trapezoid ABCD is therefore the line segment EF with endpoints E(2, 0) and F(2, 4).