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        	The vertices of a triangle are A(-1,-1),B(3,5),C(-4,1). The internal and external angle bisectors of the triangle through A cut the side BC at E,F respectively. Then the true statements among the following are	The abscissa  of E is -5/3 The ordinate of E is -3 	   The abscissa  of F is -11     	  The ordinate of F is 7/3
3 months ago

## Answers : (2)

							A(– 1, – 1) , B(3,5) , C(– 4,1)Equation of line through A and B is y + 1 = {(5+1)/(3+1)} (x + 1) after solving, we get 3x – 2y + 1 = 0. (two point form)Equation of line through A and C is y + 1 = {(1+1)/(-4+1)} (x + 1) after solving, we get 2x + 3y + 5 = 0.Equations of angle bisectors of lines through A and B & A and C are 3x – 2y + 1  =   (2x + 3y + 5)   i.e.  3x – 2y + 1 = 2x + 3y + 5   and   3x – 2y + 1 = – (2x + 3y + 5)x – 5y – 4 = 0  and  5x + y + 6 = 0. These lines are perpendicular. So, a good idea to distinguish internal and external bisectors is to roughly plotA, B, C and observe that x – 5y – 4 = 0 is the equation of external bisector and

2 months ago
							5x + y + 6 = 0 is the equation of internal bisector.Equation of line through B and C using two-point form is 4x – 7y + 23 = 0.E is the point of intersection of 5x + y + 6 = 0 and 4x – 7y + 23 = 0 while F is the point of intersection ofx – 5y – 6 = 0 and 4x – 7y + 23 = 0.You will get E(– 5/3 , 7/3)  and  F(– 11 , – 3).So, options a and c are correct.

2 months ago
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