If the three lines x-3y=p, ax+2y=q and ax+y=r form a right-angled triangle then:

Question

If the three lines $x-3y=p,\ ax+2y=q$ and $ax+y=r$ form a right-angled triangle then:

Accepted Answer

Suppose $ax+2y=q$ is perpendicular to $x-3y=p$ (slope $\dfrac13$): slope of $ax+2y=q$ is $-\dfrac a2$:
$$-\frac a2\times\frac13=-1 \implies a=6$$

Checking option A with $a=6$: $36-54+18=0$

Solutions · 1