Question

DEFG is a rhombus.

G has coordinates (9,1).
The eqution of diagonal DF is y=1/2x-1.
Find the equation of the diagonal EG.
Give your answer in the form y=ax+b

Answer 1

`y=-2x+19`

Explanation:

we know that

The diagonals of a rhombus are perpendicular

so

diagonal DF is perpendicular to diagonal EG

see the attached figure to better understand the problem

The equation of the diagonal DF is
`y=(1)/(2)x-1`

The slope of the diagonal DF is
`m=(1)/(2)`

Remember that

If two lines are perpendicular, then their slopes are opposite reciprocal (the product of their slopes is equal to -1)

so

The slope of the diagonal EG is equal to
`m=-2`

Find the equation in point slope form of the diagonal EG

`y-y1=m(x-x1)`

we have

`m=-2`

`G(9,1)`

substitute

`y-1=-2(x-9)`

Convert to slope intercept form

isolate the variable y

`y-1=-2x+18`

`y=-2x+18+1`

`y=-2x+19`