Mathematics: What is the length of the midsegment of the trapezoid made by the vertices a(0, 5), b(3, 3), c(5, -2) and d(-1, 2). show equations and all work that leads to your answer.

What is the length of the midsegment of the trapezoid

Ответ:

faithcalhoun

17.01.2022

Draw an accurate picture of the trapezoid.

The parallel bases are clearly DC and AB.

The Distance formula between 2 points P(a, b) and Q(c, d) states that:

$|PQ|= \sqrt{ (a-c)^{2} + (b-d)^{2} }$

Using this formula we find:

$|AB|= \sqrt{ (0-3)^{2} + (5-3)^{2} }=\sqrt{ 9+4}= \sqrt{ 13}$

$|CD|= \sqrt{ (5-(-1))^{2} + (-2-2)^{2} }=\sqrt{ 36+16}=\sqrt{52}=2\sqrt{13}=$

The length of the midsegment of a trapezoid is

$\frac{|base_1|+|base_2|}{2}= \frac{\sqrt{ 13}+2\sqrt{ 13}}{2}= \frac{3\sqrt{13}}{2}$

$\frac{3\sqrt{13}}{2}$

What is the length of the midsegment of the trapezoid made by the vertices a(0, 5), b(3, 3), c(5, -2

What is the length of the midsegment of the trapezoid made by the vertices a(0, 5), b(3, 3), c(5, -2

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Ответ:

treaustin6978

31.05.2020

Mathematics

Step-by-step explanation:

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What is the length of the midsegment of the trapezoid made by the vertices a(0, 5), b(3, 3), c(5, -2) and d(-1, 2). show equations and all work that leads to your answer.

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