<p>in the xy-coordinate plane, point (a,b) lies on a circle with center at (0,0). which of the following could be the radius of the circle
I. a
II. b
III. (a^2+b^2)^1/2 </p>
<p>A) I only
B) II only
C) III only
D) I and III only
E) I, II, and III</p>
<p>I picked C, but the answer is E
I don't understand how a or b can be the radius if the center is at (0,0)
What does it mean by "lies on a circle". I mean, does it mean the point lies on the circumference of the circle or anywhere in the circle including the circumference?</p>
<p>Try doing it this way. The equation of a circle is: x^2 + y^2 = R^2 where R is the radius. Can the radius be a? Well yes … that’s the point (a, 0) Can the radius be b? Yes … that the point (0, b). Can the radius be sqrt (a^2 + b^2). Yes also … that’s the point (a, b).</p>
<p>The question is “could it be”. It’s not “must it be”. Or stated differently are there values for a and b for which the assertion is true.</p>
<p>Draw the circle on the x-y plane, and try the various combinations. It should become clear.</p>
<p>Fogcity has the right idea, but the sqrt(a^2+b^2) is not (a,b). The distance from the origin to point (a,b) is of magnitude sqrt(a^2+b^2)… you need to apply vector logic… but that is irrelevant here.</p>
<p>Suppose the radius was actually 13. You can have the point (13,0) [the right-most point on the circle], the point (0,13) [the top of the circle], or the point (5, 12) [somewhere between the top and right, along the circle in the first quadrant]. All three of those are on the circle of radius 13. Thus, a=13, b=13, and (a^2+b^2)^1/2=13, all of which are the radius of the circle.</p>