Question

Find the exact length of the midsegment of the trapezoid with the vertices $S(-2,\ 4),\ T(-2,-4),\ U(3,-2),\ V(13,\ 10)$ .

Answer 1

Answer:

Find the exact length of the midsegment of the trapezoid with the vertices $S(-2,\ 4),\ T(-2,-4),\ U(3,-2),\ V(13,\ 10)$ .

Step-by-step explanation:

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Finrewerrrrtrdrd the exact length of the midsegment of the trapezoid with the vegdagkhyrrrrtices $S(-2,\ 4),\ T(-2,-4),\ U(3,-2),\ V(13,\ 10)$ .

Answer 2

Answer:

The length of the exact midsegment of the trapezoid is 11.6.

Step-by-step explanation:

Given,

The vertices of trapeziod are S(-2,4), T(-2,-4), U(3,-2) and V(13,10).

We have to find the exact length of the mid-segment of the trapezoid.

Half of the lengths of the two parallel sides, ST and UV, make up the length of the mid-segment of a trapezoid.

So, the length of ST is

$ST = \sqrt{(x_{2} - x_{1} )^{2} + (y_{2} - y_{1} )^{2} }\\\\ST = \sqrt{((-2) - (-2) )^{2} + ((-4) - 4} )^{2} }\\\\ST = \sqrt{0 + (-8 )^{2} }\\\\ST = \sqrt{64} \\\\ST = 8$

and the length of UV is

$UV = \sqrt{(x_{2} - x_{1} )^{2} + (y_{2} - y_{1})^{2} } \\\\UV = \sqrt{(13 - 3 )^{2} + ((-2) - 10)^{2} } \\\\UV = \sqrt{(10 )^{2} + (-12)^{2} } \\\\UV = \sqrt{100 + 144 } \\\\UV = 15.62$

Now, the mid-segment of trapezoid STUV

midsegment = (ST + UV)/2

midsegment = (8 + 15.62)/2

midsegment = 11.6

Hence, the length of the midsegment of a trapezoid is 11.6.

To know more about the trapezoid, click on the link below:

https://brainly.in/question/19909617

To know more about the midsegment, click on the link below:

https://brainly.in/question/50060242

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