Answer:
Explanation:
A. To plot the circles x^2+y^2=4 and x^2+y^2=1 on the same coordinate plane, we can use the standard form of the equation of a circle:
For x^2+y^2=4, the radius is 2 and the center is at the origin (0,0).
For x^2+y^2=1, the radius is 1 and the center is also at the origin (0,0)
B. To find the image of any point on x^2+y^2=4 under the transformation (x,y) to (1/2x,1/2y), we can substitute the values of x and y from the original equation into the transformation rule. Let's take the point (2,0) as an example:
(1/2x,1/2y) = (1/22, 1/20) = (1,0)
Therefore, the point (2,0) will go to the ordered pair (1,0).
C. We can notice that x^2+y^2=1 is a smaller circle that is completely contained within x^2+y^2=4, which is a larger circle. The smaller circle is a dilation of the larger one using the origin as a center and a scale factor of 1/2. This means that every point on the smaller circle is half the distance from the origin as the corresponding point on the larger circle. In other words, the smaller circle is a scaled-down version of the larger one.