Question 104741
Line 1 is through (2,3) and (11,6).
Line 2 is through points (2,3) and (-3, 18).
For lines to be perpendicular, their slopes are negative reciprocals,
{{{m[2]=-(1/m[1])}}} or
{{{m[1]m[2]=-1}}}
Let's calculate the slope of both lines and see if this relationship holds.
The formula for the slope is :
{{{m=(y[2]-y[1])/(x[2]-x[1])}}}
For Line 1,
{{{m[1]=(y[2]-y[1])/(x[2]-x[1])}}}
{{{m[1]=(6-3)/(11-2)}}}
{{{m[1]=3/9}}}
{{{m[1]=1/3}}}
For Line 2,
{{{m[2]=(y[2]-y[1])/(x[2]-x[1])}}}
{{{m[2]=(18-3)/(-3-2)}}}
{{{m[2]=-3}}}
When we look at the product of their slopes
{{{m[1]m[2]=1/3(-3)=-1}}}
We find that they are negative reciprocals and therefore the lines are perpendicular, as you can see by the graph below. 

{{{drawing( 300, 300, -5, 20, -5, 20,grid( 1 ),red(line(2,3,-3,18)),blue(line( 2, 3, 11, 6)))}}}