If the parallel sides of a trapezoid are contained by the lines and , find the equation of the line that contains the midsegment. Show equations and all work that leads to your answer.

Is the question complete?

y=m1*m2=-1

To find the equation of the line that contains the midsegment of a trapezoid, we first need to understand what a midsegment is.

In a trapezoid, the midsegment is a segment that connects the midpoints of the non-parallel sides. It is parallel to the bases of the trapezoid and has a length equal to the average of the lengths of the bases.

Let's label the given trapezoid as ABCD, with AB and CD being the parallel sides and AD and BC being the non-parallel sides. We can assume that the coordinates of the vertices are as follows:

A(x₁, y₁)
B(x₂, y₂)
C(x₃, y₃)
D(x₄, y₄)

Since we are given that the parallel sides AB and CD are contained by the lines y = mx + b₁ and y = mx + b₂ respectively, we can write the equations of these lines as:

AB: y = mx + b₁
CD: y = mx + b₂

To find the midpoints of the non-parallel sides, we can use the midpoint formula:

Midpoint of AD = ((x₁ + x₄) / 2, (y₁ + y₄) / 2)
Midpoint of BC = ((x₂ + x₃) / 2, (y₂ + y₃) / 2)

The slope of the midsegment can be found by taking the difference of the y-coordinates of the midpoints over the difference of the x-coordinates of the midpoints:

Slope of Midsegment = (y₂ + y₃ - y₁ - y₄) / (x₂ + x₃ - x₁ - x₄)

Finally, to find the equation of the line that contains the midsegment, we can use the point-slope form of a line:

y - y₁ = mMid(x - x₁)

where mMid is the slope of the midsegment and (x₁, y₁) is one of the midpoints. Plugging in the slope and midpoint values, we can simplify the equation to its final form.

Since we don't have the coordinates of the vertices of the trapezoid, we are unable to provide a specific equation. However, by following these steps and substituting the respective coordinates, you can determine the equation of the line that contains the midsegment of the given trapezoid.