SOLUTION: How far from the line 3x+2y=5 is the point of intersection of x+y=5 and x - y=3?

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Question 1145499: How far from the line 3x+2y=5 is the point of intersection of x+y=5 and x - y=3?
Answer by ikleyn(52824) About Me  (Show Source):
You can put this solution on YOUR website!
.
The intersection point is easy to find : for it, add and subtract the given equations. You will get the intersection point (4,1).


To find its distance from the line 3x + 2y = 5, use this formula


    d = abs%28Ap+%2B+Bq+%2BC%29%2Fsqrt%28A%5E2%2BB%5E2%29,     (1)


which is valid for any point (p,q) in a coordinate plane and any line Ax + By + C = 0.


In your case, p= 4, q= 1, A = 3, B= 2, C= -5,  so the distance is


    d = abs%283%2A4+%2B+2%2A1+-+5%29%2Fsqrt%283%5E2%2B2%5E2%29 = 9%2Fsqrt%2813%29 units.

Solved.

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Regarding the formula (1), see the lesson
    - The distance from a point to a straight line in a coordinate plane
    - HOW TO calculate the distance from a point to a straight line in a coordinate plane
    - Using formula for the distance from a point to a straight line in a plane to solve word problems
    - OVERVIEW of lessons on the distance from a point to a straight line in a coordinate plane
in this site.