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Question

Find the equations to the altitudes of the triangle whose angular points are A (2, -2), B (1, 1) and C (-1, 0).


Solution

AD, BE and CF are the three altitudes of the triangleWe know,Slope of AD×Slope of BC=1,AD passes through A(2, -2)Slope of BE×Slope of AC=1,AD passes through B(1, 1)Slope of CF×Slope of AB=1,AD passes through C(-1, 0)Slope of Bc=0111=12=12 Slope of AD=2Slope of AC=0(2)12=23=23 Slope of BE=32Slope of AB=1+212=21=3 Slope of CF=13So, for AD, we haveyy1=m(xx1) y(2)=2(x2) y+2=2x+4 2x+y2=0And, for BE, we haveyy1=m(xx1) y1=32(x1) [2y3x+1=0] 3x2y1=0And, for CF, we haveyy1=m(xx1) y0=13(x+1) x3y+1=0

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