Graph Points

lessonbunny.com

Answer Key & Explanations

Graph Points · Grade 5 · Worksheet 1

1. Mere is designing a rectangular community garden on a coordinate plane. Each unit on the grid represents 1 meter. She marks the four corners of the garden at points (2, 3), (11, 3), (11, 9), and (2, 9). What is the area of the garden in square meters? Answer: 54 Solution: Identify the coordinates of the four corners: (2, 3), (11, 3), (11, 9), and (2, 9). Find the length of the rectangle. The length is the horizontal distance between the left and right sides.
   Full step-by-step solution

   Step 1: Identify the coordinates of the four corners: (2, 3), (11, 3), (11, 9), and (2, 9). Step 2: Find the length of the rectangle. The length is the horizontal distance between the left and right sides. The x-coordinates are 2 and 11. Subtract: 11 - 2 = 9 meters. Step 3: Find the width of the rectangle. The width is the vertical distance between the bottom and top sides. The y-coordinates are 3 and 9. Subtract: 9 - 3 = 6 meters. Step 4: Multiply length by width to find the area: 9 x 6 = 54 square meters. The answer is 54.

2. Liam is helping his teacher arrange desks in their classroom. He places the first desk at coordinate (3, 4) on the grid map. Then he places another 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: Identify the starting coordinates of the first desk. The first desk is at (3, 4). "2 units to the right" means we add 2 to the x-coordinate.
   Full step-by-step solution

   Let's go step-by-step. Step 1: Identify the starting coordinates of the first desk. The first desk is at (3, 4). Step 2: Understand the movement for the second desk. "2 units to the right" means we add 2 to the x-coordinate. "3 units down" means we subtract 3 from the y-coordinate (because moving down decreases the y-value on a grid). Step 3: Apply the movement to the x-coordinate. Starting x = 3 Add 2 → 3 + 2 = 5 So new x = 5. Step 4: Apply the movement to the y-coordinate. Starting y = 4 Subtract 3 → 4 - 3 = 1 So new y = 1. Step 5: Write the new coordinates. The second desk is at (5, 1). Final answer: (5, 1)

3. Noah is drawing a rectangular sandbox on a coordinate grid. He marks three corners at (2, 3), (2, 8), and (9, 8). What are the coordinates of the missing fourth corner? Answer: (9, 3) Solution: List the given points: (2, 3), (2, 8), and (9, 8). Notice that (2, 3) and (2, 8) share the same x-coordinate (2), so they are vertically aligned.
   Full step-by-step solution

   Step 1: List the given points: (2, 3), (2, 8), and (9, 8). Step 2: Notice that (2, 3) and (2, 8) share the same x-coordinate (2), so they are vertically aligned. Step 3: Notice that (2, 8) and (9, 8) share the same y-coordinate (8), so they are horizontally aligned. Step 4: In a rectangle, opposite sides are parallel and equal. The missing fourth corner must have the same x-coordinate as (9, 8), which is 9, and the same y-coordinate as (2, 3), which is 3. Step 5: Therefore, the missing corner is at (9, 3). The answer is (9, 3).

4. Plot point (6, 8). Answer: Point plotted at x = 6, y = 8 Solution: Start at the origin (0, 0) on the coordinate plane. The first number is 6, so move 6 units to the right along the x-axis. The second number is 8, so from that position, move 8 units up along the y-axis.
   Full step-by-step solution

   Step 1: Start at the origin (0, 0) on the coordinate plane. Step 2: The first number is 6, so move 6 units to the right along the x-axis. Step 3: The second number is 8, so from that position, move 8 units up along the y-axis. Step 4: Draw a dot at this location. The point (6, 8) is now plotted. The answer is the point (6, 8).

5. Liam is creating a treasure map on a coordinate plane. He marks the treasure chest at point (3, 7). He then marks a large oak tree 4 units to the right and 2 units down from the treasure chest. What are the coordinates of the oak tree? Answer: (7, 5) Solution: 1. The treasure chest is at (3, 7). Coordinates are written as (x, y), where x is the horizontal position and y is the vertical position.
   Full step-by-step solution

   Let's go step-by-step. 1. The treasure chest is at (3, 7). Coordinates are written as (x, y), where x is the horizontal position and y is the vertical position. 2. The oak tree is 4 units to the right of the treasure chest. Moving right means increasing the x-coordinate. So, new x = old x + 4 = 3 + 4 = 7. 3. The oak tree is 2 units down from the treasure chest. Moving down means decreasing the y-coordinate. So, new y = old y - 2 = 7 - 2 = 5. 4. Therefore, the oak tree coordinates are (7, 5).

6. Olivia is designing a small garden on a coordinate grid. She plants a rose bush at point (3, 5) and a tulip at point (7, 5). She wants to place a sunflower at a point that forms a right angle with the rose bush and tulip, with the right angle at the rose bush. The sunflower must have an x-coordinate of 3. What are the coordinates of the sunflower? Answer: (3, 9) Solution: Plot the rose bush at (3, 5) and the tulip at (7, 5). These two points share the same y-coordinate (5), so they are on a horizontal line.
   Full step-by-step solution

   Step 1: Plot the rose bush at (3, 5) and the tulip at (7, 5). These two points share the same y-coordinate (5), so they are on a horizontal line. Step 2: For a right angle at the rose bush, the third point must be on a vertical line through (3, 5), because a vertical line and a horizontal line meet at a right angle. Step 3: The sunflower must have an x-coordinate of 3, which matches the vertical line. Step 4: Choose a y-coordinate different from 5 to make a vertical segment. Since the garden is in the first quadrant and we want a reasonable garden layout, pick a y-coordinate above the rose bush. Step 5: A common choice is 9, giving the point (3, 9). Step 6: Check: The segment from (3, 5) to (7, 5) is horizontal. The segment from (3, 5) to (3, 9) is vertical. They meet at (3, 5) forming a right angle. The answer is (3, 9).

7. 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.

8. Mason is drawing a rectangular playground on a coordinate plane for a school project. The four corners of the playground are at points (2, 9), (10, 9), (10, 3), and (2, 3). If each unit on the grid represents 2 meters, what is the perimeter of the playground in meters? Answer: 56 Solution: Find the length of the rectangle using the x-coordinates. The bottom side goes from (2, 3) to (10, 3), so length = 10 - 2 = 8 units. Find the width of the rectangle using the y-coordinates.
   Full step-by-step solution

   Step 1: Find the length of the rectangle using the x-coordinates. The bottom side goes from (2, 3) to (10, 3), so length = 10 - 2 = 8 units. Step 2: Find the width of the rectangle using the y-coordinates. The left side goes from (2, 3) to (2, 9), so width = 9 - 3 = 6 units. Step 3: Calculate the perimeter in units. Perimeter = 2 × (length + width) = 2 × (8 + 6) = 2 × 14 = 28 units. Step 4: Convert to meters using the scale (1 unit = 2 meters). 28 units × 2 meters/unit = 56 meters. The perimeter of the playground is 56 meters.