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treytonmesser
26.05.2021 •
Mathematics
Find the length of midsegment YZ in trapezoid ABCD when A(-5,-6) B(-6,-2) C(-4,0) and D(3,2)
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Ответ:
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) =![\frac{1}{2}(AD+BC)](/tpl/images/1348/1665/27343.png)
By using expression for the length of a segment between two points,
Length of a segment =![\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}](/tpl/images/1348/1665/60cfb.png)
Distance between two points A(-5, -6) and D(3, 2),
AD =![\sqrt{(3+5)^2+(2+6)^2}](/tpl/images/1348/1665/ffeb7.png)
AD =![\sqrt{64+64}](/tpl/images/1348/1665/2ffe9.png)
AD =![\sqrt{128}](/tpl/images/1348/1665/d26e6.png)
AD =![8\sqrt{2}](/tpl/images/1348/1665/fa28b.png)
Distance between B(-6, -2) and C(-4, 0)
BC =![\sqrt{(-6+4)^2+(-2-0)^2}](/tpl/images/1348/1665/cc3b3.png)
BC =![\sqrt{8}](/tpl/images/1348/1665/6ace2.png)
BC =![2\sqrt{2}](/tpl/images/1348/1665/fd7b4.png)
Therefore, m(YZ) =![\frac{1}{2}(8\sqrt{2}+2\sqrt{2})](/tpl/images/1348/1665/2dc12.png)
=![\frac{1}{2} (10\sqrt{2})](/tpl/images/1348/1665/2f779.png)
=![5\sqrt{2}](/tpl/images/1348/1665/3ab78.png)
Option C will be the answer.
Ответ:
2 two-thirds are in four-thirds because 4 divided by 2 is 2