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Answer-

The length of the midsegment of this trapezoid is 8 units.

Solution-

Trapezium Midpoint Theorem-

Mid segment of a trapezoid is equal to half of sum of its two parallel sides.

So,

[tex]\text{Length of mid segment}=\dfrac{1}{2}(AB+CD)[/tex]

Applying distance formula,

[tex]AB=\sqrt{(7-2)^2+(4-4)^2}=\sqrt{(5)^2+(0)^2}=\sqrt{(5)^2}=5[/tex]

[tex]CD=\sqrt{(9+2)^2+(-1+1)^2}=\sqrt{(11)^2+(0)^2}=\sqrt{(11)^2}=11[/tex]

Hence,

[tex]\text{Length of mid segment}=\dfrac{1}{2}(5+11)=\dfrac{1}{2}(16)=8[/tex]

Answer:  The length of the mid-segment of the trapezoid is 8 units.

Step-by-step explanation:  We are given to find the length of the mid-segment of the trapezoid ABCD in the figure.

The co-ordinates of the vertices of trapezoid ABCD are

A(2, 4), B(7, 4), C(9, -1) and D(-2, -1).

A line segment which joins mid points of two leg of trapezoid is called the mid segment of the trapezoid.

We have the TRAPEZOID MID-SEGMENT THEOREM. It states as follows:

The length of the mid segment of a trapezoid is equal to half of sum of its two parallel sides.

In trapezoid ABCD, AB and CD are the parallel sides.

The lengths of the sides AB and CD are calculated using distance formula as follows:

[tex]AB=\sqrt{(7-2)^2+(4-4)^2}=\sqrt{5^2}5~\textup{units},\\\\CD=\sqrt{(9-(-2)^2+(-1+1)^2)}=\sqrt{11^2}}=11~\textup{units}.[/tex]

Therefore, the length of the mid-segment is

[tex]l=\dfrac{AB+CD}{2}=\dfrac{5+11}{2}=\dfrac{16}{2}=8~\textup{units}.[/tex]

Thus, the length of the mid-segment is 8 units.

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