Question

If A(1, 4) , B(2, -3) and C(-1, -2) are the vertices of a ∆ ABC , find equation of right bisector of side BC

Answer 1

Let A(1,4),B(2,−3) and C(−1,−2) be the vertices of a △ABC

Let D be the midpoint of BC and let DE⊥BC

Then the coordinates of D are (

2

2−1

​

,

2

−3−3

​

)⇒(

2

1

​

,

2

−5

​

)

slope of BC=

−1−2

−2+3

​

=

3

−1

​

. Let the slope of DE be m

Then, m×

3

−1

​

=−1⇒m=3

thus, slope of DE is 3

Equation of DE is DE=

x−

2

1

​

y+

2

5

​

​

=3⇒

2x−1

2y+5

​

=3

⇒2y+5=6x−3⇒2y−6x=−8⇒y−3x+4=0⇒3x−y−4=0