SOLUTION: what is the distance between the origin and the line x+y=2? A.1 B.sqrt2 C.2sqrt2 D.2 Ithink it's A.1

Algebra ->  Inequalities -> SOLUTION: what is the distance between the origin and the line x+y=2? A.1 B.sqrt2 C.2sqrt2 D.2 Ithink it's A.1      Log On


   

Question 309149: what is the distance between the origin and the line x+y=2?
A.1 B.sqrt2 C.2sqrt2 D.2
Ithink it's A.1
Answer by texttutoring(324) About Me  (Show Source):
You can put this solution on YOUR website!
The answer is B. sqrt 2.

Draw the line, and then connect a new perpendicular line from the origin to the line. It should make a 90 degree angle.

You now have two mini triangles inside a larger triangle. The larger triangle has legs of 2 and 2. This means it has angles of 45 degrees. It is isosceles.

You can now use this angle of the top smaller triangle to find the distance from origin to line.

cos(45) = x / 2
2*cos(45) = x
x = 1. 4142 = sqrt(2)

You could also do this with the special triangle (45-45-90) instead of with Cosine(45).

Hopefully my descriptions of the graph make some sense. Let me know if they don't!