MATH SOLVE

3 months ago

Q:
# If triangle ABC is dilated by a scale factor of 2 with a center of dilation at vertex C, how does the perimeter of A'B'C' compare with the perimeter of ABC? A) The perimeter of A'B'C' is 2 times the perimeter of ABC. B) The perimeter of A'B'C' is 4 times the perimeter of ABC. C) The perimeter of A'B'C' is 6 times the perimeter of ABC. D) The perimeter of A'B'C' is 8 times the perimeter of ABC.

Accepted Solution

A:

Scaling triangle ABC with a scale factor of 2 will result in the image A'B'C' having sides which are twice the size of the sides of ABC.

Let the size of the sides of ABC be x, y and z, then the perimeter of ABC is x + y + z.

Dilation of ABC with a scale factor of 2 will result in the image A'B'C' with sides, 2x, 2y, and 2z, with perimeter 2x + 2y + 2z = 2(x + y + z) = 2 times the perimeter of ABC.

Let the size of the sides of ABC be x, y and z, then the perimeter of ABC is x + y + z.

Dilation of ABC with a scale factor of 2 will result in the image A'B'C' with sides, 2x, 2y, and 2z, with perimeter 2x + 2y + 2z = 2(x + y + z) = 2 times the perimeter of ABC.