Question

Jaycee draws a sequence of squares on the coordinate plane. First she draws a square in the center with corners at 2,2 spots and dilates it using (x,y)->(3x,3y). Then she uses this same transformation to dilate the image. She continues dilating each image in this way to draw a total of 6 squares. What dilation could she use to map the first square she draws directly to the last square she draws?

Answer 1

This is based on understanding what dilation means in a graph transformation.

The dilation from first square directly to sixth square will be; (x,y) -> (243, 243)

• In transformations, dilation of an object involves producing an image of the object that is the same shape but not the same size.

This means that if we want to dilate a square, we will produce a bigger square of a different size.

• We are told one corner of the first square she drew is (2, 2). This means that one side of the square is 2 units as the four sides of a square are equal.

• For the second square, she dilates the first one using (x, y) -> (3x, 3y).

This means the corner that was (2, 2) will now be (3 × 2), (3 × 2) = (6, 6)

• For the third square, it will be; (3 × 6), (3 × 6) = (18, 18)

• For the fourth square, it will be; (3 × 18), (3 × 18) = (54, 54)

• For the fifth square, it will be; (3 × 54), (3 × 54) = (162, 162)

• For the sixth square, it will be; (3 × 162), (3 × 162) = (486, 486)

Since first square was (2, 2), then it means dilation from first square directly to sixth square will be; (x,y) -> (486/2, 486/2)

⇒ (x,y) -> (243, 243)

Read more at; brainly.com/question/2523916