Question

# The equations of the perpendicular bisectors of the sides AB and AC of a triangle ABC are x−y+5=0 and x+2y=0 respectively. If the co-ordinates of A are (1,−2), then the equation of BC is

A
23x+14y40=0
B
14x+23y40=0
C
23x14y+40=0
D
None of these

Solution

## The correct option is B 14x+23y−40=0∵AB line is perpendicular to EO(perpendicular bisector to side AB) and passes through vertex A, Equation of AB::x+y+1=0 Coordinates of E=(x1+12,y1−22) Which is also intersection point of AB with x−y+5=0(EO line equation) So, x1+12=−3; y1−22=2⇒(x1,y1)≡(−7,6) similarly equation of AC::y=2x−4 and coordinates of F=(x2+12,y2−22) Which is also intersection point of AC with x+2y=0(F0 line equation) So, x2+12=85; y2−22=−45⇒(x2,y2)≡(11/5,2/5) So, the equation of sideBC: y−6=2/5−611/5+7(x+7)⇒14x+23y−40=0Mathematics

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