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Transformation Sequences

Grade 8 · Geometry · Worksheet 2

  1. A triangle has vertices at A(2, 1), B(5, 1), and C(3, 4) on a coordinate plane. It undergoes the following sequence of transformations: first, it is reflected across the x-axis; second, it is translated 3 units to the left; third, it is rotated 90° counterclockwise about the origin. What are the coordinates of the final image of vertex C? Answer: ______________
  2. (3² × 4) - √144 = ? Answer: ______________
  3. Liam is designing a rectangular garden with a length of 12 feet and a width of 8 feet. He wants to create a scale drawing where 1 inch represents 2 feet. What will be the perimeter of his scale drawing in inches?
    Answer: ______________
  4. Liam is designing a rectangular garden with a length of 12 feet and a width of 8 feet. He wants to create a scale drawing where 1 inch represents 2 feet. What will be the perimeter of his garden in the scale drawing?
    Answer: ______________
  5. (4³ ÷ 8) + (√144 × 2) = ? Answer: ______________
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Answer Key & Explanations

Transformation Sequences · Grade 8 · Worksheet 2

  1. A triangle has vertices at A(2, 1), B(5, 1), and C(3, 4) on a coordinate plane. It undergoes the following sequence of transformations: first, it is reflected across the x-axis; second, it is translated 3 units to the left; third, it is rotated 90° counterclockwise about the origin. What are the coordinates of the final image of vertex C? Answer: (1, -6) Solution: A transformation sequence applies several geometric operations to a shape. A reflection flips the shape over a line, changing its orientation. A translation slides the shape without rotating it.
    Full step-by-step solution

    A transformation sequence applies several geometric operations to a shape. A reflection flips the shape over a line, changing its orientation. A translation slides the shape without rotating it. A rotation turns the shape around a fixed point. To find the final position of a vertex, you apply each transformation in order to its coordinates, using the rules for each type of transformation.

  2. (3² × 4) - √144 = ? Answer: 24 Solution: Calculate 3 squared. 3² = 3 × 3 = 9. Multiply the result by 4.
    Full step-by-step solution

    Let's solve step by step. Step 1: Calculate 3 squared. 3² = 3 × 3 = 9. Step 2: Multiply the result by 4. 9 × 4 = 36. Step 3: Find the square root of 144. √144 = 12, because 12 × 12 = 144. Step 4: Subtract the square root from the earlier result. 36 − 12 = 24. Final answer: 24

  3. Liam is designing a rectangular garden with a length of 12 feet and a width of 8 feet. He wants to create a scale drawing where 1 inch represents 2 feet. What will be the perimeter of his scale drawing in inches? Answer: 20 Solution: Actual length = 12 feet Actual width = 8 feet Scale: 1 inch on the drawing = 2 feet in real life So, to convert real feet to drawing inches, divide by 2.
    Full step-by-step solution

    Let's go step-by-step. --- **Step 1: Understand the actual garden dimensions** Actual length = 12 feet Actual width = 8 feet --- **Step 2: Understand the scale** Scale: 1 inch on the drawing = 2 feet in real life So, to convert real feet to drawing inches, divide by 2. --- **Step 3: Find the drawing dimensions in inches** Drawing length = 12 feet / 2 = 6 inches Drawing width = 8 feet / 2 = 4 inches --- **Step 4: Find the perimeter of the drawing** Perimeter formula for a rectangle: \( P = 2 \times (\text{length} + \text{width}) \) So, \( P = 2 \times (6 + 4) \) \( P = 2 \times 10 \) \( P = 20 \) inches --- **Final answer:** 20

  4. Liam is designing a rectangular garden with a length of 12 feet and a width of 8 feet. He wants to create a scale drawing where 1 inch represents 2 feet. What will be the perimeter of his garden in the scale drawing? Answer: 20 inches Solution: Find the actual perimeter of the garden. The garden is a rectangle with length 12 feet and width 8 feet. Perimeter formula for a rectangle: P = 2 × (length + width) So, P = 2 × (12 + 8) = 2 × 20 = 40 feet.
    Full step-by-step solution

    Step 1: Find the actual perimeter of the garden. The garden is a rectangle with length 12 feet and width 8 feet. Perimeter formula for a rectangle: P = 2 × (length + width) So, P = 2 × (12 + 8) = 2 × 20 = 40 feet. The actual perimeter is 40 feet. Step 2: Understand the scale. The scale is 1 inch on the drawing represents 2 feet in real life. That means: 1 inch (drawing) = 2 feet (real). Step 3: Convert the actual perimeter to the drawing's perimeter. We have actual perimeter = 40 feet. Since 2 feet in real life = 1 inch in drawing, we divide the actual perimeter in feet by 2 to get the drawing's perimeter in inches: 40 feet ÷ 2 = 20 inches. Step 4: Conclusion. The perimeter of the garden in the scale drawing is 20 inches.

  5. (4³ ÷ 8) + (√144 × 2) = ? Answer: 32 Solution: Calculate 4³ = 4 × 4 × 4 = 64 Calculate 64 ÷ 8 = 8 Calculate √144 = 12 Calculate 12 × 2 = 24 Add the results: 8 + 24 = 32 The answer is 32.
    Full step-by-step solution

    Step 1: Calculate 4³ = 4 × 4 × 4 = 64 Step 2: Calculate 64 ÷ 8 = 8 Step 3: Calculate √144 = 12 Step 4: Calculate 12 × 2 = 24 Step 5: Add the results: 8 + 24 = 32 The answer is 32.