Graph Points

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Answer Key & Explanations

Graph Points · Grade 5 · Worksheet 1

1. Sophia is designing a rectangular flower bed on a coordinate grid. She marks three corners at (1, 7), (9, 7), and (1, 2). What are the coordinates of the fourth corner she needs to complete the rectangle? Answer: (9, 2) Solution: Identify the given points: A = (1, 7), B = (9, 7), C = (1, 2). In a rectangle, opposite sides are parallel and equal. The x-coordinates of A and C are both 1 (left side).
   Full step-by-step solution

   Step 1: Identify the given points: A = (1, 7), B = (9, 7), C = (1, 2). Step 2: In a rectangle, opposite sides are parallel and equal. The x-coordinates of A and C are both 1 (left side). The x-coordinate of B is 9, so the fourth corner D must have x-coordinate 9 (right side). Step 3: The y-coordinates of A and B are both 7 (top side). The y-coordinate of C is 2, so the fourth corner D must have y-coordinate 2 (bottom side). Step 4: Therefore, D = (9, 2). The coordinates of the fourth corner are (9, 2).

2. Liam is helping his teacher set up desks in the classroom. He needs to arrange them in rows and columns. If he places the first desk at the starting point (0, 0) on his grid map, and the second desk 3 units to the right and 2 units up from the first, what are the coordinates of the second desk? Answer: (3, 2) Solution: The first desk is at coordinates (0, 0). That means the x-coordinate is 0 and the y-coordinate is 0. Interpret the movement for the second desk.
   Full step-by-step solution

   Let's go step by step. Step 1: Understand the starting point. The first desk is at coordinates (0, 0). That means the x-coordinate is 0 and the y-coordinate is 0. Step 2: Interpret the movement for the second desk. The problem says: "3 units to the right" — moving right means increasing the x-coordinate. So, starting from x = 0, add 3: x = 0 + 3 = 3. Step 3: "2 units up" — moving up means increasing the y-coordinate. So, starting from y = 0, add 2: y = 0 + 2 = 2. Step 4: Combine the new coordinates. The second desk is at (x, y) = (3, 2). Step 5: Final answer: (3, 2)

3. Aroha is drawing a map of her neighborhood on a coordinate grid. Her house is at point (9, 10), and the library is at point (9, 3). If each unit on the grid represents 8 meters, what is the straight-line distance in meters from her house to the library? Answer: 56 Solution: Identify the coordinates of the house and library. House: (9, 10), Library: (9, 3). Since the x-coordinates are the same (both 9), the points are vertically aligned.
   Full step-by-step solution

   Step 1: Identify the coordinates of the house and library. House: (9, 10), Library: (9, 3). Step 2: Since the x-coordinates are the same (both 9), the points are vertically aligned. The distance in units is the difference in the y-coordinates: 10 - 3 = 7 units. Step 3: Each unit on the grid represents 8 meters. So the actual distance is 7 units × 8 meters/unit = 56 meters. The straight-line distance from Aroha's house to the library is 56 meters.

4. Plot point (8, 7) on the coordinate plane. What are the coordinates of point A if it is located 2 units to the right and 3 units up from (8, 7)? Answer: (10, 10) Solution: Start at point (8, 7). The x-coordinate is 8 and the y-coordinate is 7. Move 2 units to the right.
   Full step-by-step solution

   Step 1: Start at point (8, 7). The x-coordinate is 8 and the y-coordinate is 7. Step 2: Move 2 units to the right. This increases the x-coordinate by 2: 8 + 2 = 10. Step 3: Move 3 units up. This increases the y-coordinate by 3: 7 + 3 = 10. Step 4: The new coordinates are (10, 10). The answer is (10, 10).

5. Liam is drawing a map of his neighborhood on a coordinate plane. The library is at point (3, 7) and the park is at point (9, 7). Each unit on the grid represents 1 block. How many blocks apart are the library and the park? Answer: 6 Solution: Identify the coordinates of the library: (3, 7) and the park: (9, 7). Notice that both points have the same y-coordinate (7). This means they are on the same horizontal line.
   Full step-by-step solution

   Step 1: Identify the coordinates of the library: (3, 7) and the park: (9, 7). Step 2: Notice that both points have the same y-coordinate (7). This means they are on the same horizontal line. Step 3: To find the distance between them, subtract the x-coordinates: 9 - 3 = 6. Step 4: Since each unit represents 1 block, the distance is 6 blocks. The answer is 6.

6. Plot point (9, 4) on a coordinate grid. Answer: (9, 4) Solution: Start at the origin (0, 0). The first number is 9, so move 9 units to the right along the x-axis. The second number is 4, so from that position, move 4 units up along the y-axis.
   Full step-by-step solution

   Step 1: Start at the origin (0, 0). Step 2: The first number is 9, so move 9 units to the right along the x-axis. Step 3: The second number is 4, so from that position, move 4 units up along the y-axis. Step 4: Draw a point at this location and label it (9, 4). The answer is (9, 4).

7. Emma is drawing a map of her classroom on a coordinate grid. She places the reading corner at point (1, 3) and the art table at point (7, 9). Each unit on the grid represents 1 meter. Emma wants to place a bookshelf exactly halfway between the reading corner and the art table. What are the coordinates of the point where the bookshelf should go? Answer: (4, 6) Solution: Find the midpoint between the reading corner (1, 3) and the art table (7, 9). Step 2: To find the x-coordinate of the midpoint, add the x-coordinates of the two points and divide by 2: (1 + 7) / 2 = 8 / 2 = 4.
   Full step-by-step solution

   Step 1: Find the midpoint between the reading corner (1, 3) and the art table (7, 9). Step 2: To find the x-coordinate of the midpoint, add the x-coordinates of the two points and divide by 2: (1 + 7) / 2 = 8 / 2 = 4. Step 3: To find the y-coordinate of the midpoint, add the y-coordinates of the two points and divide by 2: (3 + 9) / 2 = 12 / 2 = 6. Step 4: The midpoint is at (4, 6). The answer is (4, 6).

8. Plot point (4, 8) on the coordinate plane. What are the coordinates of point A if it is located 2 units to the right and 3 units down from (4, 8)? Answer: (6, 5) Solution: Start at point (4, 8). The x-coordinate is 4 and the y-coordinate is 8. Move 2 units to the right.
   Full step-by-step solution

   Step 1: Start at point (4, 8). The x-coordinate is 4 and the y-coordinate is 8. Step 2: Move 2 units to the right. Moving right increases the x-coordinate: 4 + 2 = 6. Step 3: Move 3 units down. Moving down decreases the y-coordinate: 8 - 3 = 5. Step 4: The new coordinates are (6, 5). The answer is (6, 5).