Graph Points

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Answer Key & Explanations

Graph Points · Grade 5 · Worksheet 2

1. Plot point (7, 3) on the coordinate plane. What is the x-coordinate? Answer: 7 Solution: Identify the ordered pair: (7, 3). The first number in the pair is the x-coordinate, which tells how far to move right from the origin (0,0). The x-coordinate is 7.
   Full step-by-step solution

   Step 1: Identify the ordered pair: (7, 3). Step 2: The first number in the pair is the x-coordinate, which tells how far to move right from the origin (0,0). Step 3: The x-coordinate is 7. The answer is 7.

2. Liam is helping his teacher set up desks in the classroom. He places the first desk at the coordinate point (3, 4) on a grid map of the room. He then places a second desk 2 units to the right and 3 units down from the first desk. What are the coordinates of the second desk? Answer: (5, 1) Solution: The first desk is at (3, 4). x-coordinate = 3 y-coordinate = 4 - 2 units to the right → This means we add 2 to the x-coordinate.
   Full step-by-step solution

   Let's go step-by-step. --- **Step 1: Identify the starting point** The first desk is at (3, 4). That means: x-coordinate = 3 y-coordinate = 4 --- **Step 2: Understand the movement** The second desk is placed: - 2 units to the right → This means we **add 2** to the x-coordinate. - 3 units down → This means we **subtract 3** from the y-coordinate (because down means decreasing y). --- **Step 3: Apply the movement to the coordinates** Starting coordinates: (3, 4) **For x-coordinate:** 3 + 2 = 5 **For y-coordinate:** 4 − 3 = 1 --- **Step 4: Write the new coordinates** The second desk is at (5, 1). --- **Final answer:** (5, 1)

3. Liam is creating a treasure map for his friends. He places the treasure at point (3, 5) on a coordinate grid. If he starts at the origin (0, 0) and moves right 3 units, how many units must he move up to reach the treasure? Answer: 5 Solution: 1. The treasure is at point (3, 5). This means the x-coordinate is 3 and the y-coordinate is 5.
   Full step-by-step solution

   Let's go step-by-step. 1. The treasure is at point (3, 5). This means the x-coordinate is 3 and the y-coordinate is 5. 2. Liam starts at the origin (0, 0). 3. He moves right 3 units. Moving right changes the x-coordinate. Start: (0, 0) → After moving right 3 units: (3, 0). 4. Now he is at (3, 0), but the treasure is at (3, 5). Since the x-coordinate is already 3, he only needs to move vertically (up) to match the y-coordinate. 5. Current y-coordinate = 0 Treasure y-coordinate = 5 Difference = 5 - 0 = 5. 6. So he must move up 5 units to reach the treasure. Answer: 5

4. Olivia is drawing a map of her neighborhood on a coordinate grid. She places her house at point (3, 5) and the library at point (7, 1). If each unit on the grid represents 1 mile, how many miles does Olivia travel if she walks directly from her house to the library in a straight line? Round your answer to the nearest whole mile. Answer: 6 Solution: Find the horizontal difference: 7 - 3 = 4 units. Step 2: Find the vertical difference: 5 - 1 = 4 units. Step 3: Use the Pythagorean theorem: distance squared = 4^2 + 4^2 = 16 + 16 = 32.
   Full step-by-step solution

   Step 1: Find the horizontal difference: 7 - 3 = 4 units. Step 2: Find the vertical difference: 5 - 1 = 4 units. Step 3: Use the Pythagorean theorem: distance squared = 4^2 + 4^2 = 16 + 16 = 32. Step 4: Take the square root: distance = sqrt(32). Step 5: sqrt(32) = 5.656... Step 6: Round to the nearest whole mile: 6 miles. The answer is 6.

5. Emma plots three points on a coordinate grid: Point A at (1, 5), Point B at (9, 5), and Point C at (9, 1). She connects the points in order A to B to C and back to A to form a triangle. What are the coordinates of the point that would complete a rectangle if Emma adds a fourth point D? Answer: (1, 1) Solution: Identify the coordinates of the three given points: A (1, 5), B (9, 5), C (9, 1). Notice that A and B share the same y-coordinate (5), so they form a horizontal side.
   Full step-by-step solution

   Step 1: Identify the coordinates of the three given points: A (1, 5), B (9, 5), C (9, 1). Step 2: Notice that A and B share the same y-coordinate (5), so they form a horizontal side. Step 3: B and C share the same x-coordinate (9), so they form a vertical side. Step 4: For a rectangle, the fourth point D must have the same x-coordinate as A (which is 1) and the same y-coordinate as C (which is 1). Step 5: Therefore, D is at (1, 1). Step 6: Check: The points (1,5), (9,5), (9,1), (1,1) form a rectangle with all right angles. The answer is (1, 1).

6. (3.75 × 4) + (18 ÷ 0.6) = ? Answer: 45 Solution: Calculate the first parentheses: 3.75 × 4 = 15 Calculate the second parentheses: 18 ÷ 0.6 = 30 Add the results: 15 + 30 = 45 The answer is 45.
   Full step-by-step solution

   Step 1: Calculate the first parentheses: 3.75 × 4 = 15 Step 2: Calculate the second parentheses: 18 ÷ 0.6 = 30 Step 3: Add the results: 15 + 30 = 45 The answer is 45.

7. Plot point (2, 7) on the coordinate plane. What is the x-coordinate? Answer: 2 Solution: Look at the ordered pair (2, 7). The first number is the x-coordinate, which tells how far to move right from the origin (0,0). The second number is the y-coordinate, which tells how far to move up.
   Full step-by-step solution

   Step 1: Look at the ordered pair (2, 7). The first number is the x-coordinate, which tells how far to move right from the origin (0,0). The second number is the y-coordinate, which tells how far to move up. Step 2: The x-coordinate is 2. Step 3: So the answer is 2.

8. √(625) + 5³ = ? Answer: 150 Solution: Calculate the square root of 625. Since 25 × 25 = 625, √(625) = 25 Calculate 5³. This means 5 × 5 × 5 = 25 × 5 = 125 Add the results: 25 + 125 = 150 The answer is 150.
   Full step-by-step solution

   Step 1: Calculate the square root of 625. Since 25 × 25 = 625, √(625) = 25 Step 2: Calculate 5³. This means 5 × 5 × 5 = 25 × 5 = 125 Step 3: Add the results: 25 + 125 = 150 The answer is 150.