Condition for Straight Lines in Plane to be Perpendicular/Examples/Arbitrary Example 1

Examples of Use of Condition for Straight Lines in Plane to be Perpendicular
Let $\LL_1$ be the straight line whose equation in general form is given as:
 * $3 x - 4 y = 7$

Let $\LL_2$ be the straight line perpendicular to $\LL_1$ which passes through the point $\tuple {1, 2}$.

The equation for $\LL_2$ is:
 * $4 x + 3 y = 10$

Proof
From Corollary to Condition for Straight Lines in Plane to be Perpendicular, $\LL_2$ has an equation of the form:


 * $(1): \quad 4 x + 3 y = C$

We have that $\tuple {1, 2}$ is on $\LL_2$.

Hence substituting $x = 1$ and $y = 2$ into $(1)$:

Hence the result.