Question

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

Find the coordinates of midpoint D.

Answer 1

Midpoint D (-a-b , c)

Third option

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)

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=(x_1+x_2)/(2)\ , \ y=(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=(-2b+(-2a))/(2)=(2(-a-b))/(2)=-a-b\ , \ y=(2c+0)/(2)=c`

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