Grade 8 · Math

8th grade Similar shapes: a dilation plus moves worksheet

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Similar shapes: a dilation plus moves

Grade 8 Math Worksheet

NameDate

Circle the best answer, or write your answer on the line.

Bo dilates a sled sticker by 3/2 from the origin, then slides it 2 units right and 4 units down. Where does corner D(-4, 6) end? Write it like (7, -3).
Jun slides a bike sticker 2 units right and 1 unit up, then dilates it by 2 from the origin. Where does corner D(1, 2) end? Write it like (7, -3).
Kira slides a turtle sticker 1 unit right and 2 units down, then dilates it by 3/2 from the origin. Where does corner D(5, -2) end? Write it like (7, -3).
Read this first
Use this
Coordinate grid, all four quadrants, each square one unit, 20 squares across (−10 to 10), origin in the middle. Drawings A and B are both drawn. Table A | B: 10 | 6.
Drawing B is Milo's castle drawing A, dilated and turned. A's side is 10 units; B's matching side is 6 units. What is the scale factor from A to B?
Drawings A and B are both drawn. Drawing B is Noah's rocket drawing A, dilated and turned. A's side is 4 units; B's matching side is 7 units. What is the scale factor from A to B?
6.
Ren compares two window cards. Card A is 4 by 6 units; card B is 6 by 9 units. Can a dilation and moves take A onto B?
- Yes: every side grows by 2 units.
- No: the sides do not all grow by the same factor.
- Yes: every side is multiplied by 3/2.
7.
Zee compares two window cards. Card A is 4 by 6 units; card B is 6 by 8 units. Can a dilation and moves take A onto B?
- Yes: every side grows by 2 units.
- No: the sides do not all grow by the same factor.
- Yes: every side is multiplied by 3/2, so it works.
Use this
Coordinate grid, all four quadrants, each square one unit, 20 squares across (−10 to 10), origin in the middle. Cards A and B are drawn. Table A | B: 6 | 9; 8 | 11.
8.
Ari compares two quilt cards. Card A is 6 by 8 units; card B is 9 by 11 units. Can a dilation and moves take A onto B?
- Yes: every side grows by 3 units.
- No: the sides do not all grow by the same factor.
- Yes: every side is multiplied by 3/2.
Esme's boat drawing A has sides 9 and 21 units. Drawing B is A dilated and slid. B's side matching 9 is 6 units. How long is B's side matching 21?
Jun's tent drawing A has sides 6 and 9 units. Drawing B is A dilated and slid. B's side matching 6 is 8 units. How long is B's side matching 9?

8th grade Similar shapes: a dilation plus moves worksheet – printable — Print: 1 2 3 4 5 6

About this worksheet

Similar shapes: a dilation plus moves. Every version has 10 questions, and the answer key prints on the second page.

What your child will learn

I can say that a dilation plus slides, flips and turns makes a similar shape: lengths multiply by k, angles stay the same.
I can follow, undo and choose a sequence of moves that takes a shape onto a similar one.
I can tell similar from congruent, and check whether two shapes are similar by dividing matching sides.

Standard: 8.G.A.4

Words to know

similar: Same shape, maybe a different size: one is a dilation of the other, moved.

congruent: Same shape and same size.

sequence of moves: Moves done one after another, in a stated order.

matching sides: Sides in the same place on the two shapes.

scale factor from A to B: B's side ÷ A's matching side.

Common mistakes

Your child added the scale factor to a length instead of multiplying.

Your child added the size of the slide to a length, as if sliding stretched the shape. Slide a ruler across the table together: does it get longer?

Your child thought the angles grow with the shape.

What to say

Ask: if a picture is made 3 times as big, is each side 3 longer or 3 times as long?

Ask: when a photo is enlarged, do its corners get any wider?

Questions parents ask

What is the most common mistake with similar shapes: a dilation plus moves?

Your child added the scale factor to a length instead of multiplying.

How can I help my child with similar shapes: a dilation plus moves?

Ask: if a picture is made 3 times as big, is each side 3 longer or 3 times as long?

Are these 8th grade math worksheets free to print?

Yes. All 6 printable versions at each level are free to print, with the answer key, and no account is needed.

More grade 8 math

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