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Four Quadrants

Grade 6 · Mathematics · Worksheet 2

  1. Emma is helping her school's robotics team map out a racecourse on a coordinate grid. The starting point for the robot is at (-10, 15). The first checkpoint is 25 units to the right and 20 units down from the start. What are the coordinates of the first checkpoint? Answer: ______________
  2. Hana is designing a digital treasure hunt for her classmates. She places the first clue at point (-15, 12) on a coordinate plane. The treasure itself is located 20 units to the left and 18 units down from the first clue. What are the coordinates of the treasure? Answer: ______________
  3. (-3, 4) + (2, -7) = ? Answer: ______________
  4. Liam is designing a treasure map for a school project. He places the treasure chest at coordinates (-3, 4) on a coordinate plane. From the treasure chest, he draws a path that goes 7 units to the right and 5 units down to mark the starting point for the treasure hunters. What are the coordinates of the starting point? Answer: ______________
  5. Aroha is plotting the locations of landmarks in her town on a coordinate plane. The town hall is at point (-9, 11). The library is located 13 units to the right and 17 units down from the town hall. What are the coordinates of the library? Answer: ______________
  6. A point is located on the coordinate plane. Its x-coordinate is the opposite of 1250, and its y-coordinate is 1800. What is the sum of the coordinates of this point? Answer: ______________
  7. Matiu is designing a video game map on a coordinate plane. He places a treasure chest at point (-8, 6). The exit portal is located 14 units to the right and 10 units down from the treasure chest. What are the coordinates of the exit portal? Answer: ______________
  8. Ava is helping her town's planning department map out locations for a new park. On a coordinate plane where each unit represents 10 meters, the proposed playground is at point (-7, 8). The picnic area is located 12 units directly east and 15 units directly south of the playground. What are the coordinates of the picnic area? Answer: ______________
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Answer Key & Explanations

Four Quadrants · Grade 6 · Worksheet 2

  1. Emma is helping her school's robotics team map out a racecourse on a coordinate grid. The starting point for the robot is at (-10, 15). The first checkpoint is 25 units to the right and 20 units down from the start. What are the coordinates of the first checkpoint? Answer: (15, -5) Solution: The starting point is at (-10, 15). Step 2: Moving 25 units to the right means adding 25 to the x-coordinate: -10 + 25 = 15. Step 3: Moving 20 units down means subtracting 20 from the y-coordinate: 15 - 20 = -5.
    Full step-by-step solution

    Step 1: The starting point is at (-10, 15). Step 2: Moving 25 units to the right means adding 25 to the x-coordinate: -10 + 25 = 15. Step 3: Moving 20 units down means subtracting 20 from the y-coordinate: 15 - 20 = -5. Step 4: The first checkpoint is at (15, -5). The answer is (15, -5).

  2. Hana is designing a digital treasure hunt for her classmates. She places the first clue at point (-15, 12) on a coordinate plane. The treasure itself is located 20 units to the left and 18 units down from the first clue. What are the coordinates of the treasure? Answer: (-35, -6) Solution: The first clue is at (-15, 12). Moving 20 units to the left means subtracting 20 from the x-coordinate: -15 - 20 = -35. Step 2: Moving 18 units down means subtracting 18 from the y-coordinate: 12 - 18 = -6.
    Full step-by-step solution

    Step 1: The first clue is at (-15, 12). Moving 20 units to the left means subtracting 20 from the x-coordinate: -15 - 20 = -35. Step 2: Moving 18 units down means subtracting 18 from the y-coordinate: 12 - 18 = -6. Step 3: The treasure is at (-35, -6). The answer is (-35, -6).

  3. (-3, 4) + (2, -7) = ? Answer: (-1, -3) Solution: We are adding two points in coordinate form: (-3, 4) and (2, -7). Identify the x-coordinates and y-coordinates separately. First point: x1 = -3, y1 = 4 Second point: x2 = 2, y2 = -7 Add the x-coordinates together.
    Full step-by-step solution

    We are adding two points in coordinate form: (-3, 4) and (2, -7). Step 1: Identify the x-coordinates and y-coordinates separately. First point: x1 = -3, y1 = 4 Second point: x2 = 2, y2 = -7 Step 2: Add the x-coordinates together. x1 + x2 = (-3) + 2 This equals -1. Step 3: Add the y-coordinates together. y1 + y2 = 4 + (-7) This equals 4 - 7 = -3. Step 4: Combine the results into a new point. The resulting point is (-1, -3). Final answer: (-1, -3)

  4. Liam is designing a treasure map for a school project. He places the treasure chest at coordinates (-3, 4) on a coordinate plane. From the treasure chest, he draws a path that goes 7 units to the right and 5 units down to mark the starting point for the treasure hunters. What are the coordinates of the starting point? Answer: (4, -1) Solution: Identify the starting location of the treasure chest. The treasure chest is at (-3, 4). x-coordinate = -3 y-coordinate = 4 Understand the movement from the treasure chest to the starting point for treasure hunters.
    Full step-by-step solution

    Let's go step-by-step. --- **Step 1: Identify the starting location of the treasure chest.** The treasure chest is at (-3, 4). That means: x-coordinate = -3 y-coordinate = 4 --- **Step 2: Understand the movement from the treasure chest to the starting point for treasure hunters.** The path goes **7 units to the right** from the treasure chest. Moving right means **increasing the x-coordinate**. So: new x = old x + 7 new x = -3 + 7 = 4 --- **Step 3: Apply the vertical movement.** The path goes **5 units down** from the treasure chest. Moving down means **decreasing the y-coordinate**. So: new y = old y - 5 new y = 4 - 5 = -1 --- **Step 4: Combine the new coordinates.** New x = 4 New y = -1 So the starting point for treasure hunters is **(4, -1)**. --- **Final Answer:** (4, -1)

  5. Aroha is plotting the locations of landmarks in her town on a coordinate plane. The town hall is at point (-9, 11). The library is located 13 units to the right and 17 units down from the town hall. What are the coordinates of the library? Answer: (-9 + 13, 11 - 17) = (4, -6) Solution: The town hall is at (-9, 11). Moving 13 units to the right means adding 13 to the x-coordinate: -9 + 13 = 4. Step 2: Moving 17 units down means subtracting 17 from the y-coordinate: 11 - 17 = -6.
    Full step-by-step solution

    Step 1: The town hall is at (-9, 11). Moving 13 units to the right means adding 13 to the x-coordinate: -9 + 13 = 4. Step 2: Moving 17 units down means subtracting 17 from the y-coordinate: 11 - 17 = -6. Step 3: The library is at (4, -6). The answer is (4, -6).

  6. A point is located on the coordinate plane. Its x-coordinate is the opposite of 1250, and its y-coordinate is 1800. What is the sum of the coordinates of this point? Answer: 550 Solution: Identify the x-coordinate. The problem says the x-coordinate is the opposite of 1250. x = -1250 Identify the y-coordinate.
    Full step-by-step solution

    Step 1: Identify the x-coordinate. The problem says the x-coordinate is the opposite of 1250. "Opposite" means the negative, so: x = -1250 Step 2: Identify the y-coordinate. The problem says the y-coordinate is 1800. So: y = 1800 Step 3: Find the sum of the coordinates. Sum = x + y Sum = (-1250) + 1800 Step 4: Compute the addition. Think of it as 1800 - 1250. 1800 - 1250 = 550 Step 5: Final answer. The sum of the coordinates is 550.

  7. Matiu is designing a video game map on a coordinate plane. He places a treasure chest at point (-8, 6). The exit portal is located 14 units to the right and 10 units down from the treasure chest. What are the coordinates of the exit portal? Answer: (-8 + 14, 6 - 10) = (6, -4) Solution: The treasure chest is at (-8, 6). Moving 14 units to the right means adding 14 to the x-coordinate: -8 + 14 = 6. Moving 10 units down means subtracting 10 from the y-coordinate: 6 - 10 = -4.
    Full step-by-step solution

    Step 1: The treasure chest is at (-8, 6). Moving 14 units to the right means adding 14 to the x-coordinate: -8 + 14 = 6. Step 2: Moving 10 units down means subtracting 10 from the y-coordinate: 6 - 10 = -4. Step 3: The exit portal is at (6, -4). The answer is (6, -4).

  8. Ava is helping her town's planning department map out locations for a new park. On a coordinate plane where each unit represents 10 meters, the proposed playground is at point (-7, 8). The picnic area is located 12 units directly east and 15 units directly south of the playground. What are the coordinates of the picnic area? Answer: (5, -7) Solution: The playground is at (-7, 8). Moving 12 units east means adding 12 to the x-coordinate: -7 + 12 = 5. Step 2: Moving 15 units south means subtracting 15 from the y-coordinate: 8 - 15 = -7.
    Full step-by-step solution

    Step 1: The playground is at (-7, 8). Moving 12 units east means adding 12 to the x-coordinate: -7 + 12 = 5. Step 2: Moving 15 units south means subtracting 15 from the y-coordinate: 8 - 15 = -7. Step 3: The picnic area is at (5, -7). The answer is (5, -7).