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

Question

Mathematics

Reuben Deleon

5 July, 06:44

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

+2

Answers (1)

Know the Answer?

Keyla · Answer 1

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

Step-by-step 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.