Graph Points

lessonbunny.com

Answer Key & Explanations

Graph Points · Grade 5 · Worksheet 3

1. 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).

2. Plot point (9, 10) on the coordinate plane. What is the x-coordinate of this point? Answer: 9 Solution: Look at the ordered pair (9, 10). 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: Look at the ordered pair (9, 10). The first number is the x-coordinate, and the second number is the y-coordinate. Step 2: The x-coordinate is 9. This means you move 9 units to the right from the origin (0, 0) along the horizontal axis. Step 3: The y-coordinate is 10, which tells you to move 10 units up from there. Step 4: The question asks only for the x-coordinate, so the answer is 9.

3. Lily is helping her teacher set up desks in the classroom. She needs to arrange them in rows and columns. If she places the first desk at point (3, 4) on the coordinate grid and the second desk at point (7, 9), how many units apart are the centers of these two desks? Answer: 6.4 Solution: To find the distance between the centers of the two desks at points (3, 4) and (7, 9), we use the distance formula. distance = square root of ( (x2 - x1)^2 + (y2 - y1)^2 ) Identify the coordinates.
   Full step-by-step solution

   To find the distance between the centers of the two desks at points (3, 4) and (7, 9), we use the distance formula. The distance formula is: distance = square root of ( (x2 - x1)^2 + (y2 - y1)^2 ) Step 1: Identify the coordinates. First desk: (x1, y1) = (3, 4) Second desk: (x2, y2) = (7, 9) Step 2: Calculate the difference in the x-coordinates. x2 - x1 = 7 - 3 = 4 Step 3: Calculate the difference in the y-coordinates. y2 - y1 = 9 - 4 = 5 Step 4: Square these differences. (4)^2 = 16 (5)^2 = 25 Step 5: Add the squared differences. 16 + 25 = 41 Step 6: Take the square root of the sum. square root of 41 Step 7: Calculate the numerical value. We know that 6^2 = 36 and 7^2 = 49. Since 41 is between 36 and 49, the square root is between 6 and 7. 6.4^2 = 40.96, which is very close to 41. Therefore, the distance is the square root of 41, which is approximately 6.4 units. Final Answer: 6.4

4. 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 center is located at point (12, 3). If Emma walks from her house directly to the community center following the grid lines (first east/west, then north/south), what is the total distance she walks in meters? Answer: 1200 Solution: Emma's house is at (5, 8) and community center is at (12, 3) Horizontal distance = |12 - 5| = |7| = 7 units Vertical distance = |3 - 8| = |-5| = 5 units Total units = 7 + 5 = 12 units Each unit represents 100 meters Total distance = 12 × 100 = 1200 meters The answer is 1200 meters.
   Full step-by-step solution

   Step 1: Find the horizontal distance between the points Emma's house is at (5, 8) and community center is at (12, 3) Horizontal distance = |12 - 5| = |7| = 7 units Step 2: Find the vertical distance between the points Vertical distance = |3 - 8| = |-5| = 5 units Step 3: Calculate the total distance along grid lines Total units = 7 + 5 = 12 units Step 4: Convert units to meters Each unit represents 100 meters Total distance = 12 × 100 = 1200 meters The answer is 1200 meters.

5. Emma is creating a treasure map on a coordinate plane for her school's math fair. She marks the starting point at (2, 5) and places the first clue 4 units to the right and 3 units down from the starting point. Then she places the treasure chest 2 units to the left and 6 units up from the first clue. What are the coordinates of the treasure chest? Answer: (4, 8) Solution: On a coordinate plane, the first number in an ordered pair represents the x-coordinate (horizontal position) and the second number represents the y-coordinate (vertical position).
   Full step-by-step solution

   On a coordinate plane, the first number in an ordered pair represents the x-coordinate (horizontal position) and the second number represents the y-coordinate (vertical position). Moving right adds to the x-value, moving left subtracts from the x-value, moving up adds to the y-value, and moving down subtracts from the y-value. This concept helps us navigate maps, graphs, and many real-world situations where position matters.

6. Sophia is drawing a map of her neighborhood on a coordinate plane. Her house is at point (6, 1), the library is at point (1, 6), and the park is at point (6, 6). If she connects these three points to form a triangle, what is the area of the triangle in square units? Answer: 12.5 Solution: Identify the points: House (6, 1), Library (1, 6), Park (6, 6). Notice that the Park (6, 6) and House (6, 1) share the same x-coordinate (6), so the vertical distance between them is 6 - 1 = 5 units.
   Full step-by-step solution

   Step 1: Identify the points: House (6, 1), Library (1, 6), Park (6, 6). Step 2: Notice that the Park (6, 6) and House (6, 1) share the same x-coordinate (6), so the vertical distance between them is 6 - 1 = 5 units. This is one leg of the right triangle. Step 3: Notice that the Park (6, 6) and Library (1, 6) share the same y-coordinate (6), so the horizontal distance between them is 6 - 1 = 5 units. This is the other leg of the right triangle. Step 4: The triangle is a right triangle with legs of 5 units and 5 units. The area of a triangle is (1/2) x base x height. Step 5: Area = (1/2) x 5 x 5 = (1/2) x 25 = 12.5 square units. The area of the triangle is 12.5 square units.

7. A treasure hunter is following coordinates to find buried treasure. The treasure is located at the point where the x-coordinate is 2.5 times the y-coordinate, and the sum of the x-coordinate and y-coordinate is 840. If both coordinates are positive whole numbers, what is the x-coordinate of the treasure location? Answer: 600 Solution: Let \( x \) = x-coordinate Let \( y \) = y-coordinate 1. "x-coordinate is 2.5 times the y-coordinate" means: \( x = 2.5 \times y \) But 2.5 = 5/2, so: \( x = (5/2) y \) 2.
   Full step-by-step solution

   Let's solve step by step. --- **Step 1: Define variables** Let \( x \) = x-coordinate Let \( y \) = y-coordinate --- **Step 2: Translate the problem into equations** From the problem: 1. "x-coordinate is 2.5 times the y-coordinate" means: \( x = 2.5 \times y \) But 2.5 = 5/2, so: \( x = (5/2) y \) 2. "Sum of x-coordinate and y-coordinate is 840" means: \( x + y = 840 \) --- **Step 3: Substitute the first equation into the second** From \( x = (5/2) y \), substitute into \( x + y = 840 \): \( (5/2) y + y = 840 \) --- **Step 4: Combine terms** \( (5/2) y + (2/2) y = 840 \) \( (7/2) y = 840 \) --- **Step 5: Solve for y** Multiply both sides by 2: \( 7y = 1680 \) Divide by 7: \( y = 1680 / 7 \) \( y = 240 \) --- **Step 6: Solve for x** \( x = (5/2) \times 240 \) \( x = 5 \times 120 \) \( x = 600 \) --- **Step 7: Check conditions** Both coordinates are positive whole numbers: \( x = 600 \), \( y = 240 \) \( x + y = 840 \) ✓ \( x = 2.5 \times y = 2.5 \times 240 = 600 \) ✓ --- **Final answer:** x-coordinate = 600

8. What are the coordinates of point Aroha? Answer: (9, 6) Solution: Start at the origin (0,0). Move right along the x-axis until you are directly below point Aroha. Count the grid lines: you move 9 units right.
   Full step-by-step solution

   Step 1: Start at the origin (0,0). Move right along the x-axis until you are directly below point Aroha. Count the grid lines: you move 9 units right. So the x-coordinate is 9. Step 2: From that position, move straight up until you reach point Aroha. Count the grid lines: you move 6 units up. So the y-coordinate is 6. Step 3: Write the ordered pair as (x, y) = (9, 6). The answer is (9, 6).