Question

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

Answer 1

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)

Answer 2

Answer:  (-a-b, c)

Step-by-step explanation:

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

$x=\dfrac{x_1+x_2}{2}\ , \ y=\dfrac{y_1+y_2}{2}$

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 $(-2b,2c)$ and  $(-2a,0)$ is given by :-

$x=\dfrac{-2b+(-2a)}{2}=\dfrac{2(-a-b)}{2}=-a-b\ , \ y=\dfrac{2c+0}{2}=c$

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