Question

3) A square has a perimeter of 200 centimeters. The square is dilated to create a square with a side length of 40 centimeters. Which algebraic representation is correct for the dilation?A (x,y) -> (4x, 4y) B (x,y) -> (5x, 5y) C (x, y) -> (5/4x, 5/4y)D (x, y) -> (0.8x, 0.8y)Help

Answer 1

SInce the square that underwent a dilation had a perimeter of 200 cm, that means that each side had a length of 200/4 = 50 cm (recall that all sides of a square are equal in size)

Then from being 50 cm long, the sides were converted to a square of sides 40 cm long. That means that the dilation converted 50 into 40. which means that each side was multiplied by 4 and divided by 5:

50 * 4 / 5 = 200 / 5 = 40

Then the SCALE factor of the dilation was 4 / 5 = 0.8

Through a dilation , eaxh point (x, y) is transformed via the product of the coordinates by the scale factor. Then for our case:

(x, y ) ---> (0.8 x, 0.8 y)

which agrees with the last option they give you (option D)