Graph Points

lessonbunny.com

Answer Key & Explanations

Graph Points · Grade 5 · Worksheet 2

1. Plot point (9, 10) on the coordinate plane. Answer: Point plotted at (9, 10) Solution: Start at the origin (0, 0). Step 2: Move 9 units to the right along the x-axis. Step 3: From that position, move 10 units up along the y-axis.
   Full step-by-step solution

   Step 1: Start at the origin (0, 0). Step 2: Move 9 units to the right along the x-axis. Step 3: From that position, move 10 units up along the y-axis. Step 4: Draw a dot at this location. The point is at (9, 10).

2. Lily is planting a rectangular garden. She marks the corners of her garden on a coordinate plane at points (2, 3), (8, 3), (8, 7), and (2, 7). If each unit on the grid represents 1 meter, what is the area of Lily's garden in square meters? Answer: 24 Solution: A = (2, 3) B = (8, 3) C = (8, 7) D = (2, 7) Points A and B have the same y-coordinate (y = 3), so AB is horizontal. Length AB = 8 - 2 = 6 units. Points B and C have the same x-coordinate (x = 8), so BC is vertical.
   Full step-by-step solution

   Let's solve this step-by-step. **Step 1: Identify the coordinates of the rectangle** The corners are: A = (2, 3) B = (8, 3) C = (8, 7) D = (2, 7) **Step 2: Determine the length and width** Points A and B have the same y-coordinate (y = 3), so AB is horizontal. Length AB = 8 - 2 = 6 units. Points B and C have the same x-coordinate (x = 8), so BC is vertical. Width BC = 7 - 3 = 4 units. **Step 3: Verify rectangle shape** Check: From A(2,3) to D(2,7) → vertical side length = 4 units. From D(2,7) to C(8,7) → horizontal side length = 6 units. So indeed length = 6 units, width = 4 units. **Step 4: Calculate area** Area of rectangle = length × width = 6 × 4 = 24 square units. **Step 5: Apply scale** Each unit on the grid = 1 meter, so area in square meters = 24. **Final Answer:** 24

3. √(900) + 5³ = ? Answer: 155 Solution: Calculate the square root of 900. Since 30 × 30 = 900, √(900) = 30 Calculate 5³. This means 5 × 5 × 5 = 25 × 5 = 125 Add the results: 30 + 125 = 155 The answer is 155.
   Full step-by-step solution

   Step 1: Calculate the square root of 900. Since 30 × 30 = 900, √(900) = 30 Step 2: Calculate 5³. This means 5 × 5 × 5 = 25 × 5 = 125 Step 3: Add the results: 30 + 125 = 155 The answer is 155.

4. Plot point (9, 8) on a coordinate plane. What is the x-coordinate? Answer: 9 Solution: Identify the ordered pair (9, 8). The first number is the x-coordinate, and the second number is the y-coordinate. Step 2: The x-coordinate is 9.
   Full step-by-step solution

   Step 1: Identify the ordered pair (9, 8). The first number is the x-coordinate, and the second number is the y-coordinate. Step 2: The x-coordinate is 9. Step 3: The answer is 9.

5. Plot point (7, 9) on the coordinate plane. What is the y-coordinate? Answer: 9 Solution: Look at the ordered pair (7, 9). The first number is the x-coordinate, and the second number is the y-coordinate. The x-coordinate is 7, which means you move 7 units to the right from the origin (0,0).
   Full step-by-step solution

   Step 1: Look at the ordered pair (7, 9). The first number is the x-coordinate, and the second number is the y-coordinate. Step 2: The x-coordinate is 7, which means you move 7 units to the right from the origin (0,0). Step 3: The y-coordinate is 9, which means you move 9 units up from that point. Step 4: The question asks for the y-coordinate only, which is 9. The answer is 9.

6. Emma is creating a map of her neighborhood on a coordinate plane where each unit represents 100 meters. Her house is located at point (5, 8) and the community park is at point (12, 3). If Emma walks directly from her house to the park in a straight line, how many meters does she walk? Round your answer to the nearest meter. Answer: 860 Solution: Identify the coordinates: Emma's house is at (5, 8) and the park is at (12, 3) Calculate the horizontal distance: 12 - 5 = 7 units Calculate the vertical distance: 8 - 3 = 5 units Use the Pythagorean theorem: distance^2 = horizontal^2 + vertical^2 distance^2 = 7^2 + 5^2 = 49 + 25 = 74 distance =…
   Full step-by-step solution

   Step 1: Identify the coordinates: Emma's house is at (5, 8) and the park is at (12, 3) Step 2: Calculate the horizontal distance: 12 - 5 = 7 units Step 3: Calculate the vertical distance: 8 - 3 = 5 units Step 4: Use the Pythagorean theorem: distance^2 = horizontal^2 + vertical^2 Step 5: distance^2 = 7^2 + 5^2 = 49 + 25 = 74 Step 6: distance = sqrt(74) ≈ 8.6023 units Step 7: Convert to meters: 8.6023 × 100 = 860.23 meters Step 8: Round to nearest meter: 860 meters The answer is 860 meters.

7. Emma is creating a map of her neighborhood on a coordinate plane where each unit represents 100 meters. She marks her house at point (5, 8) and her school at point (12, 3). If Emma walks directly from her house to school following a straight path, how many meters does she walk? Answer: 860 Solution: Identify the coordinates: House (5, 8) and School (12, 3) Calculate the horizontal distance: 12 - 5 = 7 units Calculate the vertical distance: 8 - 3 = 5 units Use the Pythagorean theorem: distance^2 = 7^2 + 5^2 Calculate: 7^2 = 49 and 5^2 = 25 Add: 49 + 25 = 74 Find the square root: sqrt(74) ≈…
   Full step-by-step solution

   Step 1: Identify the coordinates: House (5, 8) and School (12, 3) Step 2: Calculate the horizontal distance: 12 - 5 = 7 units Step 3: Calculate the vertical distance: 8 - 3 = 5 units Step 4: Use the Pythagorean theorem: distance^2 = 7^2 + 5^2 Step 5: Calculate: 7^2 = 49 and 5^2 = 25 Step 6: Add: 49 + 25 = 74 Step 7: Find the square root: sqrt(74) ≈ 8.602 units Step 8: Convert to meters: 8.602 × 100 = 860.2 meters Step 9: Round to nearest meter: 860 meters The answer is 860.

8. What are the coordinates of point A located 7 units to the right of the origin and 9 units up? Answer: (7, 9) Solution: The origin is at (0, 0). Moving 7 units to the right means the x-coordinate is 7. Moving 9 units up means the y-coordinate is 9.
   Full step-by-step solution

   Step 1: The origin is at (0, 0). Moving 7 units to the right means the x-coordinate is 7. Moving 9 units up means the y-coordinate is 9. Step 2: Write the ordered pair as (x, y) = (7, 9). The answer is (7, 9).

9. A treasure map shows a treasure chest located at point (6, 8) on a coordinate plane. If each unit on the grid represents 5 meters, how many meters away from the origin (0,0) is the treasure chest? Answer: 50 Solution: The treasure chest is at coordinates (6, 8) on a coordinate plane. The origin is at (0, 0). Each unit on the grid represents 5 meters.
   Full step-by-step solution

   Step 1: Understand the problem. The treasure chest is at coordinates (6, 8) on a coordinate plane. The origin is at (0, 0). Each unit on the grid represents 5 meters. We need to find the straight-line distance from the origin to the chest in meters. Step 2: Find the distance in coordinate units. We use the distance formula: distance = sqrt( (x2 - x1)^2 + (y2 - y1)^2 ) Here, (x1, y1) = (0, 0) and (x2, y2) = (6, 8). So: distance in units = sqrt( (6 - 0)^2 + (8 - 0)^2 ) = sqrt( 6^2 + 8^2 ) = sqrt( 36 + 64 ) = sqrt( 100 ) = 10 units. Step 3: Convert units to meters. Each unit = 5 meters. So total distance in meters = 10 units × 5 meters/unit = 50 meters. Step 4: Final answer. The treasure chest is 50 meters away from the origin.