Question

In exercises 27-30, three vertices of DEFG are given. Find the coordinates of the remaining vertices: D(-2,-4), F(0,7), G(1,0)

Answer 1

`E =`
`(-3,3)`

Explanation:

Given

Parallelogram: DEFG

`D(x_1,y_1) = (-2,-4)`

`F(x_3,y_3) = (0,7)`

`G(x_3,y_4) = (1,0)`

Required

Find the coordinates of
`E(x_2,y_2)`

To do this, we make use of mid-point formula which is:

`M = ((x_1+x_3)/(2),(y_1+y_3)/(2))= ((x_2+x_4)/(2),(y_2+y_4)/(2))`

This gives:

`((-2+0)/(2),(-4+7)/(2))= ((x_2+1)/(2),(y_2+0)/(2))`

`((-2)/(2),(3)/(2))= ((x_2+1)/(2),(y_2+0)/(2))`

Multiply through by 2

`2 * ((-2)/(2),(3)/(2))= ((x_2+1)/(2),(y_2+0)/(2))*2`

`(-2,3) = (x_2+1,y_2+0)`

`(-2,3) = (x_2+1,y_2)`

By comparison:

`-2 = x_2 + 1` and
`3= y_2`

So, we have:

`-2-1=x_2` and
`3= y_2`

`-3 = x_2` and
`3 = y_2`

This gives:

`x_2 = -3` and
`y_2 =3`

Hence, the 4th coordinate is:
`(-3,3)`