Answer:
Option C
Step-by-step explanation:
Since, Y and Z are the midpoints of sides AB and CD of the given trapezoid.
Segment YZ will the midsegment of trapezoid ABCD.
By the theorem of midsegment,
m(YZ) = [tex]\frac{1}{2}(AD+BC)[/tex]
By using expression for the length of a segment between two points,
Length of a segment = [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Distance between two points A(-5, -6) and D(3, 2),
AD = [tex]\sqrt{(3+5)^2+(2+6)^2}[/tex]
AD = [tex]\sqrt{64+64}[/tex]
AD = [tex]\sqrt{128}[/tex]
AD = [tex]8\sqrt{2}[/tex]
Distance between B(-6, -2) and C(-4, 0)
BC = [tex]\sqrt{(-6+4)^2+(-2-0)^2}[/tex]
BC = [tex]\sqrt{8}[/tex]
BC = [tex]2\sqrt{2}[/tex]
Therefore, m(YZ) = [tex]\frac{1}{2}(8\sqrt{2}+2\sqrt{2})[/tex]
= [tex]\frac{1}{2} (10\sqrt{2})[/tex]
= [tex]5\sqrt{2}[/tex]
Option C will be the answer.
