okay so the question is:
A unit circle center at the origin undergoes a series of transformations. The equation of the resulting graph is (x-3)^2+ (y+4)^2= 25 describe the transformation the unit circle underwnt
Answer:
The original circle was centered at the origin and had radius 1
The new circle is centered at (3,-4)and has radius 5.
The unit circle was moved 3 units to the right and 4 units down,and dilated (enlarged) by a factor of 5.
is this right????
Correct.
Yes, your answer is correct. The equation (x-3)^2 + (y+4)^2 = 25 represents a circle centered at (3,-4) with a radius of 5. This means that the unit circle, which is a circle centered at the origin with a radius of 1, has undergone a series of transformations.
The first transformation is a translation or shift of 3 units to the right and 4 units down. This means that every point on the unit circle has been moved 3 units to the right and 4 units down to get to the new circle.
The second transformation is a dilation or enlargement by a factor of 5. This means that every point on the unit circle has been multiplied by 5 in both the x and y directions. As a result, the radius of the circle has been multiplied by 5, changing it from 1 to 5.
So, in summary, the unit circle has undergone a translation of 3 units to the right and 4 units down, and a dilation by a factor of 5, resulting in a circle centered at (3,-4) with a radius of 5.