Four Quadrants

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Answer Key & Explanations

Four Quadrants · Grade 6 · Worksheet 1

1. Aroha is drawing a geometric figure on a coordinate plane. She plots three points: A at (-14, 9), B at (10, 9), and C at (10, -15). She then connects the points to form a right triangle. If she reflects point C across the y-axis to create point D, what are the coordinates of point D? Answer: (-10, -15) Solution: Point C is at (10, -15). Reflecting across the y-axis means the point moves horizontally to the opposite side of the y-axis. The y-coordinate stays the same: -15.
   Full step-by-step solution

   Step 1: Point C is at (10, -15). Reflecting across the y-axis means the point moves horizontally to the opposite side of the y-axis. Step 2: The y-coordinate stays the same: -15. Step 3: The x-coordinate changes sign: from 10 to -10. Step 4: The reflected point D is at (-10, -15). The answer is (-10, -15).

2. Liam is tracking the temperature changes in his city over a week. On Monday morning, the temperature was 12°C. By evening, it dropped 8°C. On Tuesday, it rose 5°C from Monday's evening temperature. On Wednesday, a cold front came in and the temperature dropped to -3°C. What was the total temperature change from Monday morning to Wednesday? Answer: -15°C Solution: Monday morning: 12°C. Temperature dropped 8°C from Monday morning. Monday evening = 12 - 8 = 4°C.
   Full step-by-step solution

   Let's go step by step. --- **Step 1: Monday morning temperature** Monday morning: 12°C. --- **Step 2: Monday evening temperature** Temperature dropped 8°C from Monday morning. Monday evening = 12 - 8 = 4°C. --- **Step 3: Tuesday temperature** It rose 5°C from Monday evening temperature. Tuesday = 4 + 5 = 9°C. --- **Step 4: Wednesday temperature** Given: On Wednesday, temperature dropped to -3°C. So Wednesday's temperature is -3°C. --- **Step 5: Find total temperature change from Monday morning to Wednesday** Change = Final temperature - Initial temperature Change = (-3) - (12) = -3 - 12 = -15°C. --- **Step 6: Interpretation** A change of -15°C means the temperature decreased by 15°C from Monday morning to Wednesday. --- **Final answer:** -15°C

3. Maria is tracking her bank account balance. She starts with $125. On Monday, she spends $45 on groceries. On Tuesday, she deposits her $60 paycheck. On Wednesday, she pays a $85 phone bill. On Thursday, she receives a $25 refund. What is her final account balance? Answer: $80 Solution: Start with the initial balance: $125 Monday - subtract $45 for groceries: $125 - $45 = $80 Tuesday - add $60 paycheck: $80 + $60 = $140 Wednesday - subtract $85 phone bill: $140 - $85 = $55 Thursday - add $25 refund: $55 + $25 = $80 Maria's final account balance is $80.
   Full step-by-step solution

   Step 1: Start with the initial balance: $125 Step 2: Monday - subtract $45 for groceries: $125 - $45 = $80 Step 3: Tuesday - add $60 paycheck: $80 + $60 = $140 Step 4: Wednesday - subtract $85 phone bill: $140 - $85 = $55 Step 5: Thursday - add $25 refund: $55 + $25 = $80 Maria's final account balance is $80.

4. Mason is mapping out a small city park on a coordinate plane. The park entrance is at point (-7, 2). The drinking fountain is located 12 units to the right and 9 units down from the entrance. What are the coordinates of the drinking fountain? Answer: (5, -7) Solution: The entrance is at (-7, 2). Moving 12 units to the right means adding 12 to the x-coordinate: -7 + 12 = 5. Step 2: Moving 9 units down means subtracting 9 from the y-coordinate: 2 - 9 = -7.
   Full step-by-step solution

   Step 1: The entrance is at (-7, 2). Moving 12 units to the right means adding 12 to the x-coordinate: -7 + 12 = 5. Step 2: Moving 9 units down means subtracting 9 from the y-coordinate: 2 - 9 = -7. Step 3: The drinking fountain is at (5, -7). The answer is (5, -7).

5. Emma is creating a map of her town on a coordinate grid. She places the library at point (-10, 15). The school is located 25 units to the right and 20 units down from the library. What are the coordinates of the school? Answer: (15, -5) Solution: The library is at (-10, 15). Moving 25 units to the right means adding 25 to the x-coordinate: -10 + 25 = 15. Step 2: Moving 20 units down means subtracting 20 from the y-coordinate: 15 - 20 = -5.
   Full step-by-step solution

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

6. Hana is helping her school's sports team plan a new obstacle course on a coordinate plane. The starting point is at (12, -15). The first obstacle is located 18 units to the left and 10 units up from the start. The second obstacle is 14 units to the right and 22 units down from the first obstacle. What are the coordinates of the second obstacle? Answer: (8, -27) Solution: Start at (12, -15). Moving 18 units to the left means subtract 18 from the x-coordinate: 12 - 18 = -6. Moving 10 units up means add 10 to the y-coordinate: -15 + 10 = -5.
   Full step-by-step solution

   Step 1: Start at (12, -15). Moving 18 units to the left means subtract 18 from the x-coordinate: 12 - 18 = -6. Moving 10 units up means add 10 to the y-coordinate: -15 + 10 = -5. So the first obstacle is at (-6, -5). Step 2: From (-6, -5), move 14 units to the right: -6 + 14 = 8. Move 22 units down: -5 - 22 = -27. Step 3: The coordinates of the second obstacle are (8, -27). The answer is (8, -27).

7. Mason is designing a coordinate grid for a new video game level. He places a power-up at point (-7, 2). A treasure chest is located 12 units to the left and 17 units down from the power-up. What are the coordinates of the treasure chest? Answer: (-19, -15) Solution: Start with the power-up coordinates: (-7, 2). Moving 12 units to the left means subtract 12 from the x-coordinate: -7 - 12 = -19. Moving 17 units down means subtract 17 from the y-coordinate: 2 - 17 = -15.
   Full step-by-step solution

   Step 1: Start with the power-up coordinates: (-7, 2). Step 2: Moving 12 units to the left means subtract 12 from the x-coordinate: -7 - 12 = -19. Step 3: Moving 17 units down means subtract 17 from the y-coordinate: 2 - 17 = -15. Step 4: Combine the new x and y coordinates: (-19, -15). The treasure chest is at (-19, -15).