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Prove the segments joining the midpoint of consecutive sides of an isosceles trapezoid form a rhombus.

Find the coordinates of midpoint D.

Prove the segments joining the midpoint of consecutive sides of an isosceles trapezoid form a rhombus Find the coordinates of midpoint D class=

Respuesta :

choixongdong

Answer:

Midpoint D (-a-b , c)

Third option

Step-by-step explanation:

Midpoint D

x = 1/2 (-2a - 2b) = -a - b

y = 1/2 (2c) = c

Midpoint D (-a-b , c)

JeanaShupp

Answer:  (-a-b, c)

Step-by-step explanation:

We know that the mid point of a line having endpoints [tex](x_1,y_1)[/tex] and  [tex](x_2,y_2)[/tex]  is given by :-

[tex]x=\dfrac{x_1+x_2}{2}\ , \ y=\dfrac{y_1+y_2}{2}[/tex]

In the given figure it can be seen that D is the midpoint of RT :

Since R(-2b , 2c)  and  T(-2a, 0)

Then , the midpoint D of a line having endpoints [tex](-2b,2c)[/tex] and  [tex](-2a,0)[/tex] is given by :-

[tex]x=\dfrac{-2b+(-2a)}{2}=\dfrac{2(-a-b)}{2}=-a-b\ , \ y=\dfrac{2c+0}{2}=c[/tex]

Hence , the coordinates of midpoint D = (-a-b, c)

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