Problema Solution
Determine the value of A so that the line whose equation is Ax+y-5=0 is perpendicular to the line containing the points (2,-6) and (-6,3)
Answer provided by our tutors
Two lines are perpendicular means their slopes are negative reciprocals.
First we will find the slope of the line containing the (2,-6) and (-6,3):
m1 = (3 - (-6))/(-6 - 2)
m1 = - 9/8
Next we will find the slope of the line Ax+y-5=0:
Ax+y-5=0
y - 5 = -Ax
y = -Ax + 5
The slope of this line is m2 = - A.
Since m1*m2 = -1 (slopes are negative reciprocals) we have:
(-9/8)*(-A) = - 1
A = 8/9