# Thread: Equation of the straight line

1. ## Equation of the straight line

The coordinates of $\displaystyle E,F$ and $\displaystyle H$ of an equilateral are $\displaystyle (3,3),(0,-1)$and $\displaystyle (6,2)$ respectively.$\displaystyle FH$ is perpendicular to $\displaystyle EG$ whereas the straight line $\displaystyle FG$ is parallel to $\displaystyle x-axis$.Find

a)the equation of straight line $\displaystyle EG$

b)the coordinates of point $\displaystyle G$

c)the equation of locus $\displaystyle R$ such that the distance of $\displaystyle R$ from point $\displaystyle E$ and $\displaystyle F$ are equal.

2. The coordinates of and of an equilateral are and respectively.
EFG is not an equilateral triangle.

3. The coordinates of and of an equilateral are and respectively.
EFG is not an equilateral triangle.

4. Originally Posted by lindros
The coordinates of $\displaystyle E,F$ and $\displaystyle H$ of an equilateral are $\displaystyle (3,3),(0,-1)$and $\displaystyle (6,2)$ respectively.$\displaystyle FH$ is perpendicular to $\displaystyle EG$ whereas the straight line $\displaystyle FG$ is parallel to $\displaystyle x-axis$.Find

a)the equation of straight line $\displaystyle EG$
Since EG is perpendicular to FH, which has slope 1/2, EG has slope -2. That means that EG has equation y= -2(x- 3)+ 3.

b)the coordinates of point $\displaystyle G$
Since FG is parallel to the x-axis, G must have the same y coordinate as F: -1. Solve -1= -2(x- 3)+ 3 to find the x coordinate.

c)the equation of locus $\displaystyle R$ such that the distance of $\displaystyle R$ from point $\displaystyle E$ and $\displaystyle F$ are equal.
This is the straight line perpendicular to EF and passing through its midpoint. EF has slope (3-(-1))/(3- 0)= 4/3 so this line has slope -3/4. The midpoint of EF is ((3+(-1))/2, (3+ 0)/2).