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Coordinate Distance

Grade 6 · Geometry · Worksheet 1

  1. Distance from (12, -27) to (12, 42)? Answer: ______________
  2. Charlotte is helping to set up a rectangular field for a community event using a coordinate grid where each unit represents 2 meters. She places two corner flags at point A (12, 7) and point B (12, 27). These two flags have the same x-coordinate. What is the actual distance, in meters, between these two flags? Answer: ______________
  3. Distance from (Aroha, 15) to (Aroha, -9)? Answer: ______________
  4. Emma is planning a hiking route on a topographic map using a coordinate grid where each unit represents 0.5 kilometers. She starts at the trailhead at point (8, 15) and hikes to a scenic overlook at point (24, 33). After enjoying the view, she continues to a waterfall at point (24, 7). What is the total distance, in kilometers, that Emma hikes on her route? Answer: ______________
  5. Emma is helping her town plan a new park. On a coordinate grid map where each unit represents 1 meter, she places a drinking fountain at point (9, 31) and a bench at point (9, 71). What is the distance, in meters, between the drinking fountain and the bench? Answer: ______________
  6. Distance from (17, -23) to (17, 41) = ? Answer: ______________
  7. Sophia is helping her school's art club create a large mural on a coordinate grid. She places the top of a tree at point (11, 61) and the bottom of the tree at point (11, 16) on the grid. Each unit on the grid represents 1 foot. What is the height of the tree in feet? Answer: ______________
  8. Distance from (21, -16) to (21, 11)? Answer: ______________
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Answer Key & Explanations

Coordinate Distance · Grade 6 · Worksheet 1

  1. Distance from (12, -27) to (12, 42)? Answer: 69 Solution: Identify the coordinates. Point A is (12, -27) and Point B is (12, 42). The x-coordinates are both 12, so the distance is vertical.
    Full step-by-step solution

    Step 1: Identify the coordinates. Point A is (12, -27) and Point B is (12, 42). The x-coordinates are both 12, so the distance is vertical. Step 2: Find the difference in y-coordinates: 42 - (-27) = 42 + 27 = 69. Step 3: Take the absolute value: |69| = 69. The distance between the points is 69 units.

  2. Charlotte is helping to set up a rectangular field for a community event using a coordinate grid where each unit represents 2 meters. She places two corner flags at point A (12, 7) and point B (12, 27). These two flags have the same x-coordinate. What is the actual distance, in meters, between these two flags? Answer: 40 Solution: Identify the coordinates: A (12, 7) and B (12, 27). Both have the same x-coordinate (12), so the distance is vertical. Find the difference in y-coordinates: 27 - 7 = 20 units.
    Full step-by-step solution

    Step 1: Identify the coordinates: A (12, 7) and B (12, 27). Both have the same x-coordinate (12), so the distance is vertical. Step 2: Find the difference in y-coordinates: 27 - 7 = 20 units. Step 3: Each unit represents 2 meters, so multiply: 20 units x 2 meters/unit = 40 meters. Final answer: 40 meters.

  3. Distance from (Aroha, 15) to (Aroha, -9)? Answer: 24 Solution: Identify the coordinates. The points are (Aroha, 15) and (Aroha, -9). Since the x-coordinates are the same (both Aroha), the distance is vertical.
    Full step-by-step solution

    Step 1: Identify the coordinates. The points are (Aroha, 15) and (Aroha, -9). Since the x-coordinates are the same (both Aroha), the distance is vertical. Step 2: Find the difference in y-coordinates: 15 - (-9) = 15 + 9 = 24. Step 3: Take the absolute value: |24| = 24. The distance is 24 units.

  4. Emma is planning a hiking route on a topographic map using a coordinate grid where each unit represents 0.5 kilometers. She starts at the trailhead at point (8, 15) and hikes to a scenic overlook at point (24, 33). After enjoying the view, she continues to a waterfall at point (24, 7). What is the total distance, in kilometers, that Emma hikes on her route? Answer: 26 Solution: Calculate the distance from trailhead (8, 15) to overlook (24, 33) Horizontal distance = 24 - 8 = 16 units Vertical distance = 33 - 15 = 18 units Distance = sqrt(16^2 + 18^2) = sqrt(256 + 324) = sqrt(580) units Calculate the distance from overlook (24, 33) to waterfall (24, 7) Horizontal…
    Full step-by-step solution

    Step 1: Calculate the distance from trailhead (8, 15) to overlook (24, 33) Horizontal distance = 24 - 8 = 16 units Vertical distance = 33 - 15 = 18 units Distance = sqrt(16^2 + 18^2) = sqrt(256 + 324) = sqrt(580) units Step 2: Calculate the distance from overlook (24, 33) to waterfall (24, 7) Horizontal distance = 24 - 24 = 0 units Vertical distance = 33 - 7 = 26 units Distance = sqrt(0^2 + 26^2) = sqrt(676) = 26 units Step 3: Convert grid units to kilometers using the scale (1 unit = 0.5 km) First segment: sqrt(580) × 0.5 ≈ 24.083 × 0.5 ≈ 12.0415 km Second segment: 26 × 0.5 = 13 km Step 4: Add the distances Total distance = 12.0415 + 13 = 25.0415 km Step 5: Round to the nearest kilometer 25.0415 km ≈ 26 km The answer is 26 kilometers.

  5. Emma is helping her town plan a new park. On a coordinate grid map where each unit represents 1 meter, she places a drinking fountain at point (9, 31) and a bench at point (9, 71). What is the distance, in meters, between the drinking fountain and the bench? Answer: 40 Solution: Identify the coordinates. The drinking fountain is at (9, 31) and the bench is at (9, 71). They share the same x-coordinate (9).
    Full step-by-step solution

    Step 1: Identify the coordinates. The drinking fountain is at (9, 31) and the bench is at (9, 71). They share the same x-coordinate (9). Step 2: Since the x-coordinates are the same, the distance is the absolute difference of the y-coordinates. Step 3: Subtract the y-coordinates: 71 - 31 = 40. Step 4: Take the absolute value: |40| = 40. Step 5: The distance between the drinking fountain and the bench is 40 meters. The answer is 40.

  6. Distance from (17, -23) to (17, 41) = ? Answer: 64 Solution: Identify the coordinates. Point A is (17, -23) and Point B is (17, 41). The x-coordinates are the same (17), so the distance is the absolute difference of the y-coordinates.
    Full step-by-step solution

    Step 1: Identify the coordinates. Point A is (17, -23) and Point B is (17, 41). The x-coordinates are the same (17), so the distance is the absolute difference of the y-coordinates. Step 2: Find the difference: 41 - (-23) = 41 + 23 = 64. Step 3: The absolute value of 64 is 64. The answer is 64.

  7. Sophia is helping her school's art club create a large mural on a coordinate grid. She places the top of a tree at point (11, 61) and the bottom of the tree at point (11, 16) on the grid. Each unit on the grid represents 1 foot. What is the height of the tree in feet? Answer: 45 Solution: Identify the two points: (11, 61) and (11, 16). They have the same x-coordinate (11), so the distance is vertical. Find the difference in the y-coordinates: 61 - 16 = 45.
    Full step-by-step solution

    Step 1: Identify the two points: (11, 61) and (11, 16). They have the same x-coordinate (11), so the distance is vertical. Step 2: Find the difference in the y-coordinates: 61 - 16 = 45. Step 3: Since each unit represents 1 foot, the height of the tree is 45 feet. The answer is 45.

  8. Distance from (21, -16) to (21, 11)? Answer: 27 Solution: Identify the coordinates. Both points have x = 21, so the distance is vertical. The y-coordinates are -16 and 11.
    Full step-by-step solution

    Step 1: Identify the coordinates. Both points have x = 21, so the distance is vertical. The y-coordinates are -16 and 11. Step 2: Find the difference in y-values: 11 - (-16) = 11 + 16 = 27. Step 3: Distance is always positive, so the distance is 27 units. The answer is 27.