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In an isosceles triangle ABC,the coordinates of the points B and C on the base BC are respectively (1,2) and (2,1).If the equation of line AB is y=2x,then equation of line AC is?

In an isosceles triangle ABC,the coordinates of the points B and C on the base BC are respectively (1,2) and (2,1).If the equation of line AB is y=2x,then equation of line AC is?

Grade:11

2 Answers

Arun
25763 Points
3 years ago
Dear Piyush
Use
|AB| = |AC|
And you will simply get your answer.
Regards
Arun (askIITians forum expert)
Rhythm Jain
43 Points
3 years ago
Hi, As we know that the perpendicular bisected of base of an isosceles triangle will always pass through the third vertex.Let the midpoint of BC be D=(3/2,3/2)As AD is perpendicular to BC so m1xm2=-1(m1=slope of the line BC, m2=slope of the line AD), => -1 x m2 = -1 => m2 = 1Now the equation of line AD will be=> (y-y1)=m(x-x1)=> (y-3/2)=(1)(x-3/2)=> y=xOn solving the equation of AB and AD we will get the vertices of the point A which is (0,0). Hence the equation of the line AC=(y-0)=(1-0/2-0)(x-0) =>2y=xHence 2y=x is the required equation.

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