Answer
TRUE
Work Step by Step
Consider the first line $ax+by=c_{1}$:
By subtacting $-ax$ from both sides, it can be rearranged to:
$by=-ax+c_{1}$
Dividing $b$ from both sides gives the equation
$y=-\frac{a}{b}x+\frac{c_{1}}{b}$.
Therefore the gradient$=-\frac{a}{b}$
Consider the second line $bx-ay=c_{2}$:
It can be rearranged to:
$bx-c_{2}=ay$
Dividing both sides by $a$ gives the equation:
$y=\frac{b}{a}x-\frac{c_{2}}{a}$
Therefore the gradient=$\frac{b}{a}$
Multiplying both gradients gives:
$\frac{b}{a}\times-\frac{a}{b}=-1$
Therefore the lines must be perpendicular
