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

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Esme's window is a rectangle with opposite corners (-8, 4) and (4, 8). It is dilated from the origin by 3/4. What is the perimeter of the image?
Jun's door is a rectangle with opposite corners (4, -4) and (8, 4). It is dilated from the origin by 5/4. What is the perimeter of the image?
the image is not drawn. Kira's rug is a rectangle with opposite corners (-4, 2) and (2, 6). It is dilated from the origin by 3/2. How many square units does the image cover?
Luz's table top is a rectangle with opposite corners (-9, -6) and (3, 3). It is dilated from the origin by 2/3. How many square units does the image cover?
the image is not drawn. Milo's quilt is a rectangle with opposite corners (-8, -4) and (4, 4). It is dilated from the origin by 1/4. How many square units does the image cover?
Coordinate grid, all four quadrants, each square one unit, 20 squares across (-10 to 10), origin in the middle. Noah's book cover is a rectangle with opposite corners (3, -6) and (6, 3). It is dilated from the origin by 4/3. How many square units does the image cover?
Pia dilates a rug design from the origin by 2/3. How many times as much area does the image cover as the original?
Tala dilates a quilt design from the origin by 4/3. How many times as much area does the image cover as the original?
Zee dilates a table design from the origin by 1/3. How many times as much area does the image cover as the original?
A right triangle on Bo's kite drawing has corners C(-6, -3), D(3, -3) and F(-6, 3). It is dilated from the origin by 2/3. How many square units does the image cover?

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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