Question

IF A(x,y) is a point on the line joining the points B(2,-3) and C(-4,5) and A is equilateral from B and C then prove that 3x-4y+7+0

Answer 1

We are going to find slope of AB

m

AB

=

−4−2

5−(−3)

⇒ m

AB

=

−6

8

∴ m

AB

=

3

−4

Now,

m

L

×m

AB

=−1

⇒ m

L

×(

3

−4

)=−1

⇒ m

L

=

4

3

The required equation,

⇒ y−y

1

=m

L

(x−x

1

)

⇒ y−(−3)=

4

3

(x−2)

⇒ 4(y+3)=3x−6

⇒ 4y+12=3x−6=0

⇒ 3x−4y−18=0