# perpendicular bisector

• Oct 19th 2011, 11:33 AM
prasum
perpendicular bisector
the equations of perpendicular bisectors of the sides AB and AC of a triangle ABC are x-y+5=0 and x+2y=0 respectively.If this point A(1,-2) the equation of the line BC is
• Oct 19th 2011, 01:24 PM
Plato
Re: perpendicular bisector
Quote:

Originally Posted by prasum
the equations of perpendicular bisectors of the sides AB and AC of a triangle ABC are x-y+5=0 and x+2y=0 respectively.If this point A(1,-2) the equation of the line BC is

Step 1. Find the point, D, where those two lines intersect.
Step 2. Find the distance, d(A,D). The is the circum-radius.
Step 3. Write the equations of the two lines through A each of which is perpendicular to one of the given lines
Step 4. Find the points on the lines in step 3 where the circum-circle insects.
Step 5: Those points are B & C.
• Oct 19th 2011, 01:46 PM
earboth
Re: perpendicular bisector
Quote:

Originally Posted by prasum
the equations of perpendicular bisectors of the sides AB and AC of a triangle ABC are h: x-y+5=0 and g: x+2y=0 respectively.If this point A(1,-2) the equation of the line BC is

1. Since $AC \perp g$ the line AC has the slope $m_{AC} = 2$. Use point-slope-formula to determine the equation of

$AC: y+2=2(x-1)$

2. $AC\ \cap g = M_{AC}$

$2x-4 = -\frac12 x~\implies~x=\frac85$

Consequently the midpoint of $\overline{AC}$ is $M_{AC}\left(\frac85\ ,\ -\frac45\right)$

Now you can determine the coordinates of point C: $C\left(\frac{11}5\ ,\ \frac25\right)$

3. The same method will give you the point B: $B(-7, 6)$

4. Use the coordinates of B and C to determine the equation of BC.