Q:

# PLEASE HURRY!!What is the length of the midsegment of this trapezoid? Enter your answer in the box. __________ units Trapezoid A B C D on the coordinate plane. The vertices of the trapezoid are A begin ordered pair negative (11,3), B begin ordered pair (0,3), C begin ordered pair (-1,-2), and D begin ordered pair (-8,-2).

Accepted Solution

A:
Since we know that trapezoid mid-segment theorem states that mid segment of a trapezoid is half the sum of trapezoid's two parallel sides.We can see that segment AB and CD are parallel. Let us find lengths of segment AB and CD using distance formula.$$Distance =\sqrt{(x_2-x_1)^{2} +(y_2-y_1)^{2}$$$$AB =\sqrt{(0--11)^{2} +(3-3)^{2}$$$$AB =\sqrt{(0+11)^{2} +(0)^{2}$$$$AB =\sqrt{(11)^{2}$$$$AB =11$$Now let us find side length CD.$$CD =\sqrt{(-1--8)^{2} +(-2--2)^{2}$$$$CD =\sqrt{(-1+8)^{2} +(-2+2)^{2}$$$$CD =\sqrt{(7)^{2} +(0)^{2}$$$$CD =\sqrt{(7)^{2}$$$$CD =7$$Let us find length of mid segment of our given trapezoid using mid segment theorem.$$\text{ Length of mid-segment}=\frac{1}{2} \times (11+7)$$$$\text{ Length of mid-segment}=\frac{1}{2} \times (18)$$$$\text{ Length of mid-segment}=9$$Therefore, length of the mid-segment of our given trapezoid is 9 units.