Worksheet 1Worksheet 2Worksheet 3

The download includes this worksheet followed by the answer key with explanations. In the print dialog choose “Save as PDF” to download.

lessonbunny.com
Name: ______________________________ Date: ______________

Scale Factor and Dilations

Grade 10 · Mathematics · Worksheet 1

  1. A triangle is drawn on a coordinate plane with vertices at A(-5, 3), B(7, 3), and C(-5, 9). Aroha dilates this triangle from the origin using a scale factor of 1/3. What are the coordinates of the dilated triangle's vertices? Express your answer as three ordered pairs: A', B', C'. Answer: ______________
  2. A kite is drawn on a coordinate plane with vertices at A(-8, 0), B(0, 6), C(8, 0), and D(0, -2). Mere dilates this kite from the origin using a scale factor of 1/4. What are the coordinates of the dilated kite's vertices? Express your answer as four ordered pairs: A', B', C', D'. Answer: ______________
  3. A right triangle is drawn on a coordinate plane with vertices at A(0,0), B(6,0), and C(0,8). The triangle is dilated from the point (2,1) with a scale factor of 3. What are the coordinates of the dilated triangle's vertices? Express your answer as three ordered pairs: A', B', C'. Answer: ______________
  4. A quadrilateral is drawn on a coordinate plane with vertices at A(-6, 2), B(2, 2), C(4, -4), and D(-4, -4). Matiu dilates this quadrilateral from the origin using a scale factor of 0.5. What are the coordinates of the dilated quadrilateral's vertices? Express your answer as four ordered pairs: A', B', C', D'. Answer: ______________
  5. Noah is a cartographer creating a digital map of a city park. The original triangular pond on his coordinate grid has vertices at A(1, 11), B(16, 21), and C(26, 6). To fit the pond into a smaller inset map on a brochure, he applies a dilation centered at the origin with a scale factor of 1/6. What are the coordinates of vertex B' after this dilation? Answer: ______________
  6. A hexagon is drawn on a coordinate plane with vertices at A(12, 0), B(18, 12), C(12, 24), D(0, 24), E(-6, 12), and F(0, 0). Hana dilates this hexagon from the origin using a scale factor of 2/3. What are the coordinates of the dilated hexagon's vertices? Express your answer as six ordered pairs: A', B', C', D', E', F'. Answer: ______________
  7. Aroha is a digital cartographer designing a map for a hiking trail. The original map shows a triangular lookout point with vertices at A(-5, 1), B(3, -7), and C(7, 9). To create a detailed inset, she applies a dilation centered at the origin with a scale factor of 3. What are the coordinates of vertex B' after this dilation? Answer: ______________
lessonbunny.com

Answer Key & Explanations

Scale Factor and Dilations · Grade 10 · Worksheet 1

  1. A triangle is drawn on a coordinate plane with vertices at A(-5, 3), B(7, 3), and C(-5, 9). Aroha dilates this triangle from the origin using a scale factor of 1/3. What are the coordinates of the dilated triangle's vertices? Express your answer as three ordered pairs: A', B', C'. Answer: (-5/3, 1), (7/3, 1), (-5/3, 3) Solution: The original vertices are A(-5, 3), B(7, 3), C(-5, 9). Step 2: Dilation from the origin with scale factor k = 1/3 means each coordinate is multiplied by 1/3. Step 3: Calculate A': (-5 * 1/3, 3 * 1/3) = (-5/3, 1).
    Full step-by-step solution

    Step 1: The original vertices are A(-5, 3), B(7, 3), C(-5, 9). Step 2: Dilation from the origin with scale factor k = 1/3 means each coordinate is multiplied by 1/3. Step 3: Calculate A': (-5 * 1/3, 3 * 1/3) = (-5/3, 1). Step 4: Calculate B': (7 * 1/3, 3 * 1/3) = (7/3, 1). Step 5: Calculate C': (-5 * 1/3, 9 * 1/3) = (-5/3, 3). Step 6: The dilated triangle's vertices are A'(-5/3, 1), B'(7/3, 1), C'(-5/3, 3).

  2. A kite is drawn on a coordinate plane with vertices at A(-8, 0), B(0, 6), C(8, 0), and D(0, -2). Mere dilates this kite from the origin using a scale factor of 1/4. What are the coordinates of the dilated kite's vertices? Express your answer as four ordered pairs: A', B', C', D'. Answer: (-2, 0), (0, 3/2), (2, 0), (0, -1/2) Solution: The original vertices are A(-8, 0), B(0, 6), C(8, 0), and D(0, -2). Dilation from the origin with scale factor k = 1/4 means each coordinate is multiplied by 1/4.
    Full step-by-step solution

    Step 1: The original vertices are A(-8, 0), B(0, 6), C(8, 0), and D(0, -2). Step 2: Dilation from the origin with scale factor k = 1/4 means each coordinate is multiplied by 1/4. Step 3: Calculate A': (-8 * 1/4, 0 * 1/4) = (-2, 0) Step 4: Calculate B': (0 * 1/4, 6 * 1/4) = (0, 6/4) = (0, 3/2) Step 5: Calculate C': (8 * 1/4, 0 * 1/4) = (2, 0) Step 6: Calculate D': (0 * 1/4, -2 * 1/4) = (0, -2/4) = (0, -1/2) Step 7: The dilated kite's vertices are A'(-2, 0), B'(0, 3/2), C'(2, 0), D'(0, -1/2).

  3. A right triangle is drawn on a coordinate plane with vertices at A(0,0), B(6,0), and C(0,8). The triangle is dilated from the point (2,1) with a scale factor of 3. What are the coordinates of the dilated triangle's vertices? Express your answer as three ordered pairs: A', B', C'. Answer: ( -4, -2), (10, -2), (-4, 22) Solution: To dilate from point (2,1), we first translate all points so that (2,1) becomes the origin.
    Full step-by-step solution

    Step 1: To dilate from point (2,1), we first translate all points so that (2,1) becomes the origin. A(0,0) becomes (0-2, 0-1) = (-2,-1) B(6,0) becomes (6-2, 0-1) = (4,-1) C(0,8) becomes (0-2, 8-1) = (-2,7) Step 2: Apply the scale factor of 3 to these translated coordinates: A: (-2,-1) × 3 = (-6,-3) B: (4,-1) × 3 = (12,-3) C: (-2,7) × 3 = (-6,21) Step 3: Translate back by adding (2,1) to each coordinate: A': (-6+2, -3+1) = (-4,-2) B': (12+2, -3+1) = (14,-2) C': (-6+2, 21+1) = (-4,22) Step 4: Verify the answer: A'(-4,-2), B'(14,-2), C'(-4,22) The dilated triangle's vertices are at (-4,-2), (14,-2), and (-4,22).

  4. A quadrilateral is drawn on a coordinate plane with vertices at A(-6, 2), B(2, 2), C(4, -4), and D(-4, -4). Matiu dilates this quadrilateral from the origin using a scale factor of 0.5. What are the coordinates of the dilated quadrilateral's vertices? Express your answer as four ordered pairs: A', B', C', D'. Answer: (-3, 1), (1, 1), (2, -2), (-2, -2) Solution: The original vertices are A(-6, 2), B(2, 2), C(4, -4), D(-4, -4). Dilation from the origin with scale factor k = 0.5 means each coordinate is multiplied by 0.5.
    Full step-by-step solution

    Step 1: The original vertices are A(-6, 2), B(2, 2), C(4, -4), D(-4, -4). Step 2: Dilation from the origin with scale factor k = 0.5 means each coordinate is multiplied by 0.5. Step 3: Calculate A': (-6 * 0.5, 2 * 0.5) = (-3, 1) Step 4: Calculate B': (2 * 0.5, 2 * 0.5) = (1, 1) Step 5: Calculate C': (4 * 0.5, -4 * 0.5) = (2, -2) Step 6: Calculate D': (-4 * 0.5, -4 * 0.5) = (-2, -2) Step 7: The dilated quadrilateral's vertices are A'(-3, 1), B'(1, 1), C'(2, -2), D'(-2, -2).

  5. Noah is a cartographer creating a digital map of a city park. The original triangular pond on his coordinate grid has vertices at A(1, 11), B(16, 21), and C(26, 6). To fit the pond into a smaller inset map on a brochure, he applies a dilation centered at the origin with a scale factor of 1/6. What are the coordinates of vertex B' after this dilation? Answer: (8/3, 7/2) or approximately (2.667, 3.5) Solution: Identify the original coordinates of vertex B: (16, 21). The dilation is centered at the origin with scale factor k = 1/6. Multiply the x-coordinate: x' = (1/6) * 16 = 16/6 = 8/3.
    Full step-by-step solution

    Step 1: Identify the original coordinates of vertex B: (16, 21). Step 2: The dilation is centered at the origin with scale factor k = 1/6. Step 3: Apply the dilation formula: (x', y') = (k * x, k * y). Step 4: Multiply the x-coordinate: x' = (1/6) * 16 = 16/6 = 8/3. Step 5: Multiply the y-coordinate: y' = (1/6) * 21 = 21/6 = 7/2. Step 6: The coordinates of vertex B' after dilation are (8/3, 7/2). As decimals: 8/3 ≈ 2.667, 7/2 = 3.5. The answer is (8/3, 7/2).

  6. A hexagon is drawn on a coordinate plane with vertices at A(12, 0), B(18, 12), C(12, 24), D(0, 24), E(-6, 12), and F(0, 0). Hana dilates this hexagon from the origin using a scale factor of 2/3. What are the coordinates of the dilated hexagon's vertices? Express your answer as six ordered pairs: A', B', C', D', E', F'. Answer: (8, 0), (12, 8), (8, 16), (0, 16), (-4, 8), (0, 0) Solution: The original vertices are A(12, 0), B(18, 12), C(12, 24), D(0, 24), E(-6, 12), F(0, 0). Dilation from the origin with scale factor k = 2/3 means each coordinate is multiplied by 2/3.
    Full step-by-step solution

    Step 1: The original vertices are A(12, 0), B(18, 12), C(12, 24), D(0, 24), E(-6, 12), F(0, 0). Step 2: Dilation from the origin with scale factor k = 2/3 means each coordinate is multiplied by 2/3. Step 3: Calculate A': (12 * 2/3, 0 * 2/3) = (8, 0) Step 4: Calculate B': (18 * 2/3, 12 * 2/3) = (12, 8) Step 5: Calculate C': (12 * 2/3, 24 * 2/3) = (8, 16) Step 6: Calculate D': (0 * 2/3, 24 * 2/3) = (0, 16) Step 7: Calculate E': (-6 * 2/3, 12 * 2/3) = (-4, 8) Step 8: Calculate F': (0 * 2/3, 0 * 2/3) = (0, 0) Step 9: The dilated hexagon's vertices are A'(8, 0), B'(12, 8), C'(8, 16), D'(0, 16), E'(-4, 8), F'(0, 0).

  7. Aroha is a digital cartographer designing a map for a hiking trail. The original map shows a triangular lookout point with vertices at A(-5, 1), B(3, -7), and C(7, 9). To create a detailed inset, she applies a dilation centered at the origin with a scale factor of 3. What are the coordinates of vertex B' after this dilation? Answer: (9, -21) Solution: Identify the original coordinates of vertex B: (3, -7) The dilation is centered at the origin with scale factor k = 3.
    Full step-by-step solution

    Step 1: Identify the original coordinates of vertex B: (3, -7) Step 2: The dilation is centered at the origin with scale factor k = 3. Step 3: Apply the dilation formula: (x', y') = (k * x, k * y) Step 4: Multiply each coordinate by 3: x' = 3 * 3 = 9, y' = 3 * (-7) = -21 Step 5: The coordinates of vertex B' after dilation are (9, -21). The answer is (9, -21).