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Question 1004256: The lines 3x+2y-10=0 is perpendicular to 2x-By+2=0.
a.) Find the value of B.
b.) Find the distance from intersection of lines to the origin.
c.) Find the equation of line having a slope of 2 which passes through the intersection of two lines.
Answer by Cromlix(4381)   (Show Source):
You can put this solution on YOUR website! Hi there,
First sort out equations into
y = mx + c form
3x + 2y - 10 = 0
2y = -3x + 10
y = -3/2x + 5
..........
2x - By + 2 = 0
-By = -2x - 2
By = 2x + 2
..........
Lines that are perpendicular
to one another have slopes that
multiply together to give -1
m1 x m2 = -1
-3/2 x m2 = -1
m2 = 2/3
..........
So B = 3
By = 2x + 2
3y = 2x + 2
y = 2/3x + 2/3
...........
Using:
3y - 2x = 2......(1)
2y + 3x = 10.....(2)
Multiply (1) by 3
Multiply (2) by 2
9y - 6x = 6......(1)
4y + 6x = 20.....(2)
Add (1) + (2)
13y .....= 26
y .......= 2
Substitute y = 2 into
2y + 3x = 10
2(2) + 3x = 10
4 + 3x = 10
3x = 6
x = 2
{2,2} Intersection.
B) Distance to (2,2) = 2root2 = 2.83 units (2 decimal places)
C) Using y - b = m(x - a)
with m = 2
(a,b) = (2,2)
y - 2 = 2(x - 2)
y - 2 = 2x - 4
y = 2x - 4 + 2
y = 2x - 2
Hope this helps :-)
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