Question

Consider the following two circles. Circle P with center (-1, 2) and radius 3 and circle Q with center (3, 4) radius 5. What sequence of transformations will carry circle P onto circle Q? Select all that apply.

A. Dilation centered at Q, followed by reflection across the y-axis
B. Dilation centered at P, followed by reflection across the y-axis and then the line y = -x + 5
C. Translation (x,y) -> (x+4, y+2), followed by dilation centered at Q
D. Dilation (x+y) -> (3/5x, 3/5y), followed by dilation centered at P
E. Reflection over x-axis followed by rotation of 270 degrees

Answer 1

Answer: Option b and Option c

Answer 2

B. Dilation centered at P, followed by reflection across the y-axis and then the line y = -x + 5

Explanation:

Circle P.

Centerat (-1, 2).

Radius of 3.

Circle Q.

Center at (3, 4).

Radius of 5.

To carry one circle onto the other, their centers and radius must be the same.

So, circle P must be shifted from (-1, 2) to (3, 4), that means the translation is 4 units to the right side and two units upside, this is the first transformation.

The second transformation must be about stretching the circle P, from a radius of 3 to a radius of 5.

Therefore, the right answer is B.