SOLUTION: Find the coordinates of the point A on the line x = –3 such that the line joining A to B (3, 5) is perpendicular to the line 2x + 5y = 12.

Algebra ->  Parallelograms -> SOLUTION: Find the coordinates of the point A on the line x = –3 such that the line joining A to B (3, 5) is perpendicular to the line 2x + 5y = 12.      Log On


   

Question 898672: Find the coordinates of the point A on the line x = –3 such that the line joining A to B (3, 5) is perpendicular to the line 2x + 5y = 12.
Answer by Edwin McCravy(20063) About Me  (Show Source):
You can put this solution on YOUR website!


We want to find the point A on the green line x = -3, such that the red
line that goes from B(3,5) down to it is perpendicular to the black
line 2x+5y=12.

Since point A is on the green line x=-3, its x-coordinate is -3.

Let it's y-coordinate be k.  So the point is A(-3,k)

We find the slope of the black line by getting it into slope-intercept
form:

2x+%2B+5y+=+12
    5y+=+-2x+%2B+12
     y+=+expr%28-2%2F5%29x+%2B+12%2F5%29 

Compare that to

      y+=+mx%2Bb, we see that the slope of the black line is -2%2F5

Therefore the slope of the red line is the reciprocal of -2%2F5 but 
with the opposite sign.  So the slope of the red line is %22%22%2B5%2F2.

Since point A is on the green line x=-3, its x-coordinate is -3.

Let its y-coordinate be k.

We use the slope-formula:

m = %28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29
where (x1,y1) = B(3,5)
and where (x2,y2) = A(-3,k)

m = %28k-5%29%2F%28-3-3%29 

5%2F2%22%22=%22%22%28k-5%29%2F%28-3-3%29

5%2F2%22%22=%22%22%28k-5%29%2F%28-6%29

Cross multiply:

2%28k-5%29%22%22=%22%225%2A%28-6%29

2k-10%22%22=%22%22-30

   2k%22%22=%22%22-20

    k%22%22=%22%22-10

So the point is A(-3,-10)

Edwin