SOLUTION: A. Find the equation of the line passing through the points (3, -5) and ( 1, -2). B. Find the equation of the line perpendicular to the line you found above and passing throu

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: A. Find the equation of the line passing through the points (3, -5) and ( 1, -2). B. Find the equation of the line perpendicular to the line you found above and passing throu      Log On


   



Question 154238: A. Find the equation of the line passing through the points (3, -5) and ( 1, -2).
B. Find the equation of the line perpendicular to the line you found above and passing throught the point ( -1, - 2)

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
(a) The formula is:

where
(3, -5) is (x%5B1%5D,y%5B1%5D)
(1, -2) is (x%5B2%5D,y%5B2%5D)
Actually, you could interchange (3, -5) and (1, -2) and you'd
still get the right answer
-------------------------------
%28y+-+%28-5%29%29+%2F+%28x+-+3%29+=+%28-2+-+%28-5%29%29+%2F+%281+-+3%29
%28y+%2B+5%29+%2F+%28x+-+3%29+=+3+%2F+%28-2%29
Multiply both sides by %28x+-+3%29%2A%28-2%29
%28-2%29%2A%28y+%2B+5%29+=+3%2A%28x+-+3%29
-2y+-+10+=+3x+-+9
-2y+=+3x+%2B+1
y+=+-%283%2F2%29x+-+1%2F2 answer
check answer:
Does the line pass through (3, -5) and (1, -2)?
-5+=+-%283%2F2%29%2A3+-+1%2F2
-5+=+-%289%2F2%29+-+1%2F2
-5+=+-5
OK
-2+=+-%283%2F2%29%2A1+-+1%2F2
-2+=+-2
OK
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(b)The slope of the line perpendicular to this
line must have a slope m%5B2%5D+=+-%281%2Fm%5B1%5D%29
where m%5B1%5D+=+-%283%2F2%29
m%5B2%5D+=+2%2F3
It passes through (-1 , -2)
I can use the point-slope formula for this
m+=+%28y+-+y%5B1%5D%29+%2F+%28x+-+x%5B1%5D%29
2%2F3+=+%28y+-+%28-2%29%29+%2F+%28x+-+%28-1%29%29
2%2F3+=+%28y+%2B+2%29+%2F+%28x+%2B+1%29
Multiply both sides by 3%2A%28x+%2B+1%29
2%2A%28x+%2B+1%29+=+3%2A%28y+%2B+2%29
2x+%2B+2+=+3y+%2B+6
3y+=+2x+-+4
y+=+%282%2F3%29x+-+4%2F3
---------------------
Does it pass through (-1, -2)?
-2+=+%282%2F3%29%2A%28-1%29+-+4%2F3
-2+=+-%282%2F3%29+-+4%2F3
-2+=+-2
OK