Question

the lines x-2y+6=0 and 2x+y+2=0 intersect at the point A .
a). find the coordinate of A
b). prove that the two lines are perpendicular.​

Answer 1

Answer:

ans of b -- If two lines are perpendicular then product of their slopes will be negative 1 , since the product of slopes of this here is negative 1 so we can say that two this two lines are perpendicular to each other.

Answer 2

Answer:

x + 2.y + 6 = 0. ………………(1).

2.x - y - 2 = 0. ………………….(2)

x/(-4+6) =y/(12+2) = 1/(-1–4).

or, x/2 = y/14 = -1/5.

or, x= -2/5. , y = -14/5. , thus , point of intersection P(-2/5, -14/5).

Let the equation of the line is y= m.x+c. ………………(3)

Line (3) passes through (-2/5, -14/5) and c=5 units (given).

-14/5 = m.(-2/5) + 5.

or, 2m/5 = 14/5 +5.

or, 2m/5= 39/5 => m. = 39/2.

Putting m= 39/2. and c = 5 in eqn.(3) the required equation of the line is:-

y = 39/2. x +5.

or, 39.x -2.y +10 = 0. Answer.