Question

Is the line through $(-2,3)$ and $(4,1)$ perpendicular to the line $3x=y+1$? Does the line $3x=y+1$ bisect the line joining of $(-2,3)$ and $(4,1)?$

Answer 1

$(-2,3),(4,1)$ $m=\frac{4+2}{1-3}=-3$

$-3(x-4)=(y-1)$

$-3x+12=y-1$

$3x+y-13=0$ is perpendicular to the line $3x-y-1=0$

P should pass through $3x=y+1$

$3=2+1$

Yes, the line bisect the join of $(-2,3)$ & $(4,1)$.