SOLUTION: The line h contains the points (6,-2) and (-4,10). The equation of the line k is ax+6y+12=0 and k is perpendicular to h. Find the value of the real number a. Please help..

Algebra ->  Points-lines-and-rays -> SOLUTION: The line h contains the points (6,-2) and (-4,10). The equation of the line k is ax+6y+12=0 and k is perpendicular to h. Find the value of the real number a. Please help..       Log On


   

Question 824810: The line h contains the points (6,-2) and (-4,10). The equation of the line k is ax+6y+12=0 and k is perpendicular to h. Find the value of the real number a. Please help..
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
The line h has the slope %2810-%28-2%29%29%2F%28-4-6%29=12%2F%28-10%29=-6%2F5.

The line, k, is also 6y=-ax-12,
y=-%28a%2F6%29x-2---------line k.

Line h perpendicular to line k means that highlight_green%28%28-6%2F5%29%2A%28-a%2F6%29=-1%29.
The typically stated rule for this is, if two perpendicular lines in a plane have slopes m%5B1%5D and m%5B2%5D, then m%5B1%5Dm%5B2%5D=-1.