Question

Show that lines x − 2y − 7 = 0 and 2x + y + 1 = 0 are perpendicular to each other. Find their point of intersection

Answer 1

Slope of the line x − 2y − 7 = 0 is

m₁ = `-"coefficient of x"/"coefficient of y" = -1/((-2)) = 1/2`

Slope of the line 2x + y + 1 = 0 is

m₂ = `-"coefficient of x"/"coefficient of y" = -2/1` = − 2

Since m₁ = m₂ = `1/2(-2)` = − 1 the lines are perpendicular to each other.

To find the point of intersection, we have to solve

x − 2y − 7 = 0   ...(1)

and 2x + y + 1 = 0  ...(2)

Multiplying equation (2) by 2, we get

4x + 2y + 2 = 0   ...(3)

Adding equations (1) and (3), we get

5x − 5 = 0

∴ x = 1

∴ from (2), 2(1) + y + 1 = 0

∴ y = −3

Hence, the point of intersection of the lines is (1, −3).