Grade 8 · Math

8th grade What a dilation does to length, perimeter and area worksheet

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What a dilation does to length, perimeter and area

Grade 8 Math Worksheet - Building Confidence

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Ari's rug design has a perimeter of 12 units and is dilated from the origin by 3/2. The table rows are 1 | 3/2 and 12 | ?. What is the new perimeter?
Bo's quilt design has a perimeter of 18 units and is dilated from the origin by 2/3. The table rows are 1 | 2/3 and 18 | ?. What is the new perimeter?
Kira's rug design covers 8 square units. It is dilated from the origin by 3/2, so the area row is 1 | 3/2 × 3/2. How many square units does the image cover?
Luz's quilt design covers 18 square units. It is dilated from the origin by 2/3, so the area row is 1 | 2/3 × 2/3. How many square units does the image cover?
Milo's book design covers 32 square units. It is dilated from the origin by 3/4, so the area row is 1 | 3/4 × 3/4. How many square units does the image cover?
Noah's window design covers 9 square units. It is dilated from the origin by 4/3, so the area row is 1 | 4/3 × 4/3. How many square units does the image cover?
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Use this
Coordinate grid, all four quadrants, each square one unit, 20 squares across (−10 to 10), origin in the middle. The rug drawing with that side marked; the image is not drawn.
One side of Pia's rug drawing runs from (-4, 2) to (2, 2). The drawing is dilated from the origin by 3/2. How long is that side on the image, in units?
One side of Ren's door drawing runs from (3, 3) to (3, 9). The drawing is dilated from the origin by 2/3. How long is that side on the image, in units?
One side of Tala's table drawing runs from (-8, -4) to (4, -4). The drawing is dilated from the origin by 3/4. How long is that side on the image, in units?
Use this
Coordinate grid, all four quadrants, each square one unit, 20 squares across (-10 to 10), origin in the middle. The window drawing with that side marked; the image is not drawn.
One side of Zee's window drawing runs from (3, -3) to (3, 3). The drawing is dilated from the origin by 4/3. How long is that side on the image, in units?

8th grade What a dilation does to length, perimeter and area worksheet – printable — Print: 1 2 3 4 5 6

About this worksheet

What a dilation does to length, perimeter and area. 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 by k multiplies every length and the perimeter by k, and the area by k × k.
I can find the new perimeter and area of a shape on the grid after a dilation, even when k is below 1.
I can work back from two areas to the scale factor, and from a new area to the old one.

Standard: state-only (CCSS 7.G.A.1 in Grade 7; related 8.G.A.3)

Words to know

dilation: Enlarging or shrinking a shape from a point, here the origin.

scale factor (k): What every length is multiplied by, from old to new.

perimeter: The distance all the way around a shape.

area: How many unit squares a shape covers.

area factor: What every area is multiplied by: k × k.

Common mistakes

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

Your child used the area factor (the scale factor times itself) for a length.

Your child multiplied an area by the scale factor once, as if it were a length.

What to say

Ask: if a picture is made 3/2 times as big, is each side 3/2 longer or 3/2 times as long?

Ask: does a perimeter cover space, or go around it?

Ask: if every side doubles, how many copies of the old rectangle fit inside?

Questions parents ask

What is the most common mistake with what a dilation does to length, perimeter and area?

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

How can I help my child with what a dilation does to length, perimeter and area?

Ask: if a picture is made 3/2 times as big, is each side 3/2 longer or 3/2 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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