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Math Help - perpendicular bisector

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    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
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    Re: perpendicular bisector

    Quote Originally Posted by prasum View Post
    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.
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    Re: perpendicular bisector

    Quote Originally Posted by prasum View Post
    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.
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