Coordinate Distance

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Answer Key & Explanations

Coordinate Distance · Grade 6 · Worksheet 2

1. Liam is tracking the temperature changes in his city over a week. On Monday morning, the temperature was 12°C. By afternoon, it rose by 8°C. Overnight, it dropped by 15°C. What was the temperature on Tuesday morning? Answer: 5°C Solution: Start with Monday morning temperature. Monday morning temperature = 12°C. Temperature rise by afternoon.
   Full step-by-step solution

   Let's go step by step. Step 1: Start with Monday morning temperature. Monday morning temperature = 12°C. Step 2: Temperature rise by afternoon. It rose by 8°C, so: Monday afternoon temperature = 12 + 8 = 20°C. Step 3: Overnight drop. From Monday afternoon to Tuesday morning, it dropped by 15°C. So: Tuesday morning temperature = 20 - 15 = 5°C. Step 4: Conclusion. The temperature on Tuesday morning was 5°C.

2. A rectangular sports field is mapped on a coordinate plane with corners at (120, 50), (480, 50), (480, 290), and (120, 290). The grounds crew needs to install a straight underground irrigation pipe that runs diagonally from the southwest corner to the northeast corner. What is the length of this diagonal irrigation pipe in meters? Answer: 410 Solution: Identify the coordinates of the southwest and northeast corners. Southwest corner is (120, 50) and northeast corner is (480, 290). Calculate the horizontal distance (length) between these points: 480 - 120 = 360 meters.
   Full step-by-step solution

   Step 1: Identify the coordinates of the southwest and northeast corners. Southwest corner is (120, 50) and northeast corner is (480, 290). Step 2: Calculate the horizontal distance (length) between these points: 480 - 120 = 360 meters. Step 3: Calculate the vertical distance (width) between these points: 290 - 50 = 240 meters. Step 4: Use the Pythagorean theorem to find the diagonal length: diagonal = sqrt(360^2 + 240^2). Step 5: Calculate 360^2 = 129,600 and 240^2 = 57,600. Step 6: Add these squares: 129,600 + 57,600 = 187,200. Step 7: Take the square root: sqrt(187,200) = 410. The length of the diagonal irrigation pipe is 410 meters.

3. 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.

4. Isabella is helping her school's art club create a large mural on a coordinate grid. She places the top-left corner of a rectangular frame at point (27, 72) and the top-right corner at point (92, 72). Each unit on the grid represents 1 centimeter. What is the width of the frame in centimeters? Answer: 65 Solution: Identify the coordinates: top-left corner (27, 72) and top-right corner (92, 72). Notice that the y-coordinates are the same (72), so the distance is horizontal. Find the difference in x-coordinates: 92 - 27 = 65.
   Full step-by-step solution

   Step 1: Identify the coordinates: top-left corner (27, 72) and top-right corner (92, 72). Step 2: Notice that the y-coordinates are the same (72), so the distance is horizontal. Step 3: Find the difference in x-coordinates: 92 - 27 = 65. Step 4: Since each unit is 1 centimeter, the width is 65 centimeters. The answer is 65.

5. Noah is helping his school's art club create a large mural on a coordinate grid. The club paints a vertical line from point A at (42, 18) to point B at (42, 74). Each unit on the grid represents 2 inches. What is the actual length, in inches, of the painted line? Answer: 112 Solution: Identify the coordinates: A = (42, 18), B = (42, 74). Both have the same x-coordinate (42), so the line is vertical. Step 2: Find the vertical distance in grid units: 74 - 18 = 56 units.
   Full step-by-step solution

   Step 1: Identify the coordinates: A = (42, 18), B = (42, 74). Both have the same x-coordinate (42), so the line is vertical. Step 2: Find the vertical distance in grid units: 74 - 18 = 56 units. Step 3: Each unit represents 2 inches, so multiply: 56 × 2 = 112 inches. The answer is 112 inches.

6. Aroha is designing a rectangular mural for her school's art wall. On the coordinate plane, the top-left corner of the mural is at (24, 32) and the bottom-right corner is at (57, 14). Aroha wants to paint a straight horizontal line across the mural at y = 32 that goes from the left edge to the right edge. What is the length of this horizontal line in units? Answer: 33 Solution: Identify the two points that define the ends of the horizontal line. The left edge of the mural at y = 32 is at (24, 32) and the right edge at y = 32 is at (57, 32).
   Full step-by-step solution

   Step 1: Identify the two points that define the ends of the horizontal line. The left edge of the mural at y = 32 is at (24, 32) and the right edge at y = 32 is at (57, 32). Step 2: Since the y-coordinates are the same (both are 32), the distance is the absolute difference in the x-coordinates. Step 3: Calculate the difference: 57 - 24 = 33. Step 4: The length of the horizontal line is 33 units. The answer is 33.

7. 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.