SOLUTION: Please help me solve this question. Find the equation of the line joining A(-1, -9)to B(6, 12) Another line passes through C(7, -5) and meets AB at right angle at D. Find the

Algebra ->  Coordinate-system -> SOLUTION: Please help me solve this question. Find the equation of the line joining A(-1, -9)to B(6, 12) Another line passes through C(7, -5) and meets AB at right angle at D. Find the      Log On


   

Question 70222: Please help me solve this question.
Find the equation of the line joining A(-1, -9)to B(6, 12)
Another line passes through C(7, -5) and meets AB at right angle at D. Find the equation of CD and calculate the coordinates of D.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
To find the slope from A(-1, -9)to B(6, 12) use
m=%2812-%28-9%29%29%2F%286-%28-1%29%29
m=21%2F7
m=3
Now use the general slope-intercept equation of a line y=mx+b and solve for b.
12=3%286%29%2BbPlug in point B(6,12) either point will work
12-18=b
b=-6
So the equation is
y=3x-6
To find the equation from C to D, we need to invert and negate the slope of our previous answer. This makes the new slope perpendicular to the old slope.
m=-1%2F3
Now plug in the point C to solve for b
-5=%28-1%2F3%29%287%29%2Bb
-5%2B7%2F3=b
b=-8%2F3
So the equation of the line that passes through CD is
y=%28-1%2F3%29x-8%2F3
To verify this answer, you can graph these lines and plot the points. A good program for this on the PC is Winplot (http://math.exeter.edu/rparris/winplot.html ) which allows quick and efficient graphing, and allows you to plot points.