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The equations of the perpendicular bisec...

The equations of the perpendicular bisectors of the sides `A Ba n dA C` of triangle `A B C` are `x-y+5=0` and `x+2y=0` , respectively. If the point `A` is `(1,-2)` , then find the equation of the line `B Cdot`

Text Solution

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The correct Answer is:
14x+23y-40=0

Since the given lines are perpendicular bisectors of the sides as shown in the figure, point B and C are the images of the point A in these lines. Therefore,
`(x_(1)-1)/(1) = (y_(1)-2)/(2) = -(2(1-4))/(1+4)`
`"and " (x_(2)-1)/(1) = (y_(2)+2)/(-1) = -(2(1+2+5))/(1+1)`
`therefore B(x_(1), y_(1))-= (11//5, 2//5) " and " C(x_(2), y_(2))-= (-7,6)`
Hence, the line passing through the points B and C is 14x+23y-40=0.
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