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

Answer:

$y=-2x+19$

Step-by-step 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 $y=\frac{1}{2}x-1$

The slope of the diagonal DF is $m=\frac{1}{2}$

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

$y-1=-2x+18$

$y=-2x+18+1$

$y=-2x+19$