SOLUTION: here is my question, the coordinates of the point have equal absolute value, the point is in teh second quadrant, and the distance of the point from teh origin is 2. x= and y= .

Algebra ->  Graphs -> SOLUTION: here is my question, the coordinates of the point have equal absolute value, the point is in teh second quadrant, and the distance of the point from teh origin is 2. x= and y= .      Log On


   

Question 13768: here is my question, the coordinates of the point have equal absolute value, the point is in teh second quadrant, and the distance of the point from teh origin is 2. x= and y= .
Answer by glabow(165) About Me  (Show Source):
You can put this solution on YOUR website!
The idea is this: the points that are a distance of 2 from the origin forms a circle with radius 2 around the origin. The equation for that circle around the origin is +x%5E2+%2B+y%5E2+=+4 because the squares of the two sides formed by the x and y coordinates add up to the square of the hypotenuse.

In the given case, since the x and y are known to be equal, then you have x%5E2+%2B+x%5E2+=+4
which means +2x%5E2+=+4 and x%5E2=2. So, x=sqrt%282%29
Since the square root can be plus or minus, the only question remaining is which is it? The answer lies in the second quadrant, which means the x value is negative and the y value is positive. So the coordinates of a point with the absolute values of the x and y values being equal that lies 2 from the origin are +-sqrt%282%29 ,+sqrt%282%29