contestada

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.

Respuesta :

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:

[tex]|PQ|= \sqrt{ (a-c)^{2} + (b-d)^{2} } [/tex]


Using this formula we find:

[tex]|AB|= \sqrt{ (0-3)^{2} + (5-3)^{2} }=\sqrt{ 9+4}= \sqrt{ 13}[/tex]

[tex]|CD|= \sqrt{ (5-(-1))^{2} + (-2-2)^{2} }=\sqrt{ 36+16}=\sqrt{52}=2\sqrt{13}=[/tex]


The length of the midsegment of a trapezoid is 

[tex] \frac{|base_1|+|base_2|}{2}= \frac{\sqrt{ 13}+2\sqrt{ 13}}{2}= \frac{3\sqrt{13}}{2}[/tex]


Answer: [tex]\frac{3\sqrt{13}}{2}[/tex]

Ver imagen eco92

Otras preguntas