SOLUTION: could i get some help with this? (a) Find the point of intersection between the following two lines: (x; y) = (1, 2) + t(4; 3); t is an element of the Real numbers (x; y) = (

Algebra ->  Decimal-numbers -> SOLUTION: could i get some help with this? (a) Find the point of intersection between the following two lines: (x; y) = (1, 2) + t(4; 3); t is an element of the Real numbers (x; y) = (      Log On


   

Question 940705: could i get some help with this?
(a) Find the point of intersection between the following two lines:
(x; y) = (1, 2) + t(4; 3); t is an element of the Real numbers
(x; y) = (2,-1) + s(1; 2); s is an element of the Real number
steps would be appreciated cheers
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
You can get the slope of the lines since you have the formula for each point.
Assume t=1 then the change in y is 3, change in x is 4 so the slope is,
m=3%2F4
So line 1 is, using the point-slope form,
y-2=%283%2F4%29%28x-1%29
y-2=%283%2F4%29x-3%2F4
y=%283%2F4%29x%2B5%2F4
Similarly for line 2,
y-%28-1%29=2%28x-2%29
y%2B1=2x-4
y=2x-5
For intersection, set the two equal to each other.
%283%2F4%29x%2B5%2F4=2x-5
3x%2B5=8x-20
-5x=-25
x=5%7D%7D%0D%0AThen%2C%0D%0A%7B%7B%7By=2%285-5
y=5
(5,5)
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