# Equation of the straight line

• Mar 26th 2010, 01:01 AM
lindros
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.
• Mar 26th 2010, 01:22 AM
sa-ri-ga-ma
• Mar 26th 2010, 01:23 AM
sa-ri-ga-ma
• Mar 26th 2010, 04:29 AM
HallsofIvy
Quote:

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.

Quote:

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.

Quote:

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).