the equations of the altitude AD, BE, CF of a triangle ABC arex +y=0, x−4y=0, 2x−y=0 respectively. the cordinates of Aare (t,−t), find the cordinates of B &amp; c. Prove tha as tvaries the locus of the centroid of the triangle ABC is theline x+5y=0

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the equations of the altitude AD, BE, CF of a triangle ABC arex +y=0, x−4y=0, 2x−y=0 respectively. the cordinates of Aare (t,−t), find the cordinates of B &amp;amp; c. Prove tha as tvaries the locus of the centroid of the triangle ABC is theline x+5y=0

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Question: the equations of the altitude AD,BE, CF of a triangle ABC are x+y=0, x−4y=0, 2x−y=0 respectively. the cordinates of A are (t,−t), find the cordinatesof B &amp;amp; c. Prove tha as t varies the locus of the centroid ofthe triangle ABC is the line x+5y=0 A is (t,-t) SINCE B LIES ON BE⋯X−4Y=0⋯ITS COORDINATES SHOULD SATISFYEQN. OF BE....HENCE LET B BE (4b,b)⋯slope of BE=14 similarly C is (c,2c)⋯.slope of CF=2 since BE is perpendicular to AEC...... slope of AC× slope of BE=−1 {(2c+t)(c−t)×(14)=−1 2c+t=−4(c−t)=−4c+4t 6c=3t c=t2.......................hence C is (t2,t) similarly..we get since AFB is perpendicular to CF slope of AB× slope of CF={−1{(b+t)}{(4b−t)}×2=−12b+2t=−4b+t6b=−t b=−t6 .....hence B is (−2t6,−t6)

the equations of the altitude AD, BE, CF of a triangle ABC arex + y = 0, x - 4y = 0, 2x - y = 0 respectively. the cordinates of Aare (t, -t), find the cordinates of B & c.

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