Question

find the equation of the Line passing through they point(4,-3) and perpendicular to the line joining the point (1,1),(2,3)​

Answer 1

Answer:

Let, A(1,1) and B(2,3)

So, the equation of AB

$\frac{x - 1}{1 - 2} = \frac{y - 1}{1 - 3}$

$or \: \frac{x - 1}{ - 1} = \frac{y - 1}{ - 2}$

or, 2(x-1) = y-1

or, 2x-2 = y-1

or, 2x-y-2+1 = 0

or, 2x-y-1 = 0..............................(1)

Now the perpendicular equation of (1)

x+2y+k = 0.……………………………(2)

Since, (4,-3) passing through (2)

4-2*3+k = 0

or, 4-6 + k = 0

or, k-2 = 0

or, k = 2

putting the value of k in (2)

x+2y+2 = 0

Hence the required answere

x+2y+2 = 0