What a dilation does to length, perimeter and area
Grade 8 Math Worksheet

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Coordinate grid, all four quadrants, each square one unit, 20 squares across (−10 to 10), origin in the middle. The rug rectangle with corners (2, 2) and (6, 4) marked; the image is not drawn.
Ari's rug is a rectangle with opposite corners (2, 2) and (6, 4). It is dilated from the origin by 3/2. What is the perimeter of the image?
Bo's quilt is a rectangle with opposite corners (-6, -3) and (6, 3). It is dilated from the origin by 2/3. What is the perimeter of the image?
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?
Coordinate grid, all four quadrants, each square one unit, 20 squares across (−10 to 10), origin in the middle. The window rectangle with corners (-8, 4) and (4, 8) marked; the image is not drawn. Coordinate grid, all four quadrants, each square one unit, 20 squares across (−10 to 10), origin in the middle. The window rectangle with corners (-8, 4) and (4, 8) marked; the image is not drawn. −10 −8 −6 −4 −2 2 4 6 8 10 −10 −9 −8 −7 −6 −5 −4 −3 −2 −1 1 2 3 4 5 6 7 8 9 10 20 squares across (-10 to 10), origin in the middle. The image is not drawn. 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?
Coordinate grid, all four quadrants, each square one unit, 20 squares across (−10 to 10), origin in the middle. The door rectangle with corners (4, -4) and (8, 4) marked; the image is not drawn. Coordinate grid, all four quadrants, each square one unit, 20 squares across (−10 to 10), origin in the middle. The door rectangle with corners (4, -4) and (8, 4) marked; the image is not drawn. Coordinate grid, 20 squares across (-10 to 10) −10 −8 −6 −4 −2 2 4 6 8 10 −10 −8 −6 −4 −2 2 4 6 8 10 0 door 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?
Coordinate grid, all four quadrants, each square one unit, 20 squares across (−10 to 10), origin in the middle. The rug rectangle with corners (-4, 2) and (2, 6) marked; the image is not drawn. Coordinate grid, all four quadrants, each square one unit, 20 squares across (−10 to 10), origin in the middle. The rug rectangle with corners (-4, 2) and (2, 6) marked; the image is not drawn. 20 squares across (-10 to 10) x y -10 10 -10 10 (-4, 2) (2, 6) each square: 1 unit 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?
Coordinate grid, all four quadrants, each square one unit, 20 squares across (−10 to 10), origin in the middle. The book rectangle with corners (3, -6) and (6, 3) marked; the image is not drawn. Coordinate grid, all four quadrants, each square one unit, 20 squares across (−10 to 10), origin in the middle. The book rectangle with corners (3, -6) and (6, 3) marked; the image is not drawn. Coordinate grid: each square one unit x y -10 0 10 10 -10 (3, -6) (6, 3) origin 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 Ari's tent drawing has corners C(-4, 2), D(2, 2) and F(-4, 6). It is dilated from the origin by 3/2. 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. Triangle CDF is drawn, with the right angle at C; the image is not drawn. Coordinate grid, all four quadrants, each square one unit, 20 squares across (−10 to 10), origin in the middle. Triangle CDF is drawn, with the right angle at C; the image is not drawn. −10 −8 −6 −4 −2 2 4 6 8 10 −10 −8 −6 −4 −2 2 4 6 8 10 0 C D F A right triangle on Esme's sled drawing has corners C(-8, -4), D(4, -4) and F(-8, 4). It is dilated from the origin by 3/4. 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. Triangle CDF is drawn, with the right angle at C; the image is not drawn. Coordinate grid, all four quadrants, each square one unit, 20 squares across (−10 to 10), origin in the middle. Triangle CDF is drawn, with the right angle at C; the image is not drawn. −10 −8 −6 −4 −2 2 4 6 8 10 −10 −8 −6 −4 −2 2 4 6 8 10 0 C D F