Coordinate Graphing

lessonbunny.com

Answer Key & Explanations

Coordinate Graphing · Grade 5 · Worksheet 1

1. Mere draws a rectangle on a coordinate plane. The vertices are at (4, 2), (4, 10), (12, 10), and (12, 2). What is the area of this rectangle in square units? Answer: 64 Solution: Identify the length of the rectangle. The points (4,2) and (4,10) have the same x-coordinate, so the distance between them is the vertical side. Length = 10 - 2 = 8 units.
   Full step-by-step solution

   Step 1: Identify the length of the rectangle. The points (4,2) and (4,10) have the same x-coordinate, so the distance between them is the vertical side. Length = 10 - 2 = 8 units. Step 2: Identify the width of the rectangle. The points (4,2) and (12,2) have the same y-coordinate, so the distance between them is the horizontal side. Width = 12 - 4 = 8 units. Step 3: Use the area formula for a rectangle: Area = length × width. Step 4: Calculate: Area = 8 × 8 = 64. The area of the rectangle is 64 square units.

2. Plot the points (5, 0), (5, 15), (20, 15), and (20, 0) on a coordinate plane. What shape is formed and what is its area? Answer: rectangle, 225 Solution: Identify the shape. The points (5,0), (5,15), (20,15), and (20,0) form a rectangle because opposite sides are parallel and all angles are right angles. Find the length.
   Full step-by-step solution

   Step 1: Identify the shape. The points (5,0), (5,15), (20,15), and (20,0) form a rectangle because opposite sides are parallel and all angles are right angles. Step 2: Find the length. The x-coordinates go from 5 to 20, so the horizontal distance is 20 - 5 = 15 units. Step 3: Find the width. The y-coordinates go from 0 to 15, so the vertical distance is 15 - 0 = 15 units. Step 4: Calculate the area. Area of a rectangle = length × width = 15 × 15 = 225 square units. The answer is rectangle, 225.

3. Liam is creating a map of his neighborhood park on a coordinate plane. He marks the playground at (2, 5), the picnic area at (8, 5), the swimming pool at (8, 1), and the basketball court at (2, 1). When Liam connects these points in order, what shape does he create and what is its perimeter? Answer: rectangle with a perimeter of 20 units Solution: Playground = (2, 5) Picnic area = (8, 5) Swimming pool = (8, 1) Basketball court = (2, 1) Order: (2, 5) → (8, 5) → (8, 1) → (2, 1) → back to (2, 5) - (2, 5) and (8, 5): same y-coordinate (y = 5) → horizontal line - (8, 5) and (8, 1): same x-coordinate (x = 8) → vertical line - (8, 1) and (2, 1):…
   Full step-by-step solution

   Let's go step-by-step. --- **Step 1: Plot the points in order** Points given: Playground = (2, 5) Picnic area = (8, 5) Swimming pool = (8, 1) Basketball court = (2, 1) Order: (2, 5) → (8, 5) → (8, 1) → (2, 1) → back to (2, 5) --- **Step 2: Identify the shape** Check horizontal and vertical alignment: - (2, 5) and (8, 5): same y-coordinate (y = 5) → horizontal line - (8, 5) and (8, 1): same x-coordinate (x = 8) → vertical line - (8, 1) and (2, 1): same y-coordinate (y = 1) → horizontal line - (2, 1) and (2, 5): same x-coordinate (x = 2) → vertical line So we have two pairs of parallel horizontal sides and two pairs of parallel vertical sides. All angles are 90° because horizontal and vertical lines are perpendicular. Thus, the shape is a rectangle. --- **Step 3: Find side lengths** Horizontal sides: From (2, 5) to (8, 5): length = 8 - 2 = 6 units From (2, 1) to (8, 1): length = 8 - 2 = 6 units Vertical sides: From (8, 5) to (8, 1): length = 5 - 1 = 4 units From (2, 1) to (2, 5): length = 5 - 1 = 4 units So rectangle dimensions: length = 6 units, width = 4 units. --- **Step 4: Calculate perimeter** Perimeter of rectangle = 2 × (length + width) = 2 × (6 + 4) = 2 × 10 = 20 units --- **Step 5: Final answer** Shape: rectangle Perimeter: 20 units **Answer:** rectangle with a perimeter of 20 units

4. Liam is designing a rectangular garden on a coordinate plane. He plots the bottom-left corner at (2, 3) and the top-right corner at (8, 7). What is the area of Liam's garden in square units? Answer: 24 Solution: Bottom-left corner: (2, 3) Top-right corner: (8, 7) The length (horizontal side) is the difference in the x-coordinates: Length = 8 - 2 = 6 units The width (vertical side) is the difference in the y-coordinates: Width = 7 - 3 = 4 units Area of a rectangle = Length × Width Area = 6 × 4 = 24…
   Full step-by-step solution

   Let's find the area of the rectangular garden step by step. **Step 1: Identify the coordinates** Bottom-left corner: (2, 3) Top-right corner: (8, 7) **Step 2: Find the length and width** The length (horizontal side) is the difference in the x-coordinates: Length = 8 - 2 = 6 units The width (vertical side) is the difference in the y-coordinates: Width = 7 - 3 = 4 units **Step 3: Calculate the area** Area of a rectangle = Length × Width Area = 6 × 4 = 24 square units **Final Answer:** 24

5. Hana is helping her school's art club create a giant mural on a coordinate grid. The mural will feature a rectangular frame for a painting. Hana plots three corners of the rectangle at points (4, 2), (12, 2), and (4, 10). If each unit on the grid represents 1 square foot, what is the area of the rectangular frame in square feet? Answer: 64 Solution: Identify the coordinates of the three given corners: (4, 2), (12, 2), and (4, 10). Find the fourth corner. The rectangle has horizontal and vertical sides.
   Full step-by-step solution

   Step 1: Identify the coordinates of the three given corners: (4, 2), (12, 2), and (4, 10). Step 2: Find the fourth corner. The rectangle has horizontal and vertical sides. The point (4, 2) and (12, 2) share the same y-coordinate, so they form a horizontal side. The point (4, 2) and (4, 10) share the same x-coordinate, so they form a vertical side. The fourth corner must be directly across from (4, 2), sharing the x-coordinate of (12, 2) and the y-coordinate of (4, 10). So the fourth corner is at (12, 10). Step 3: Find the length of the rectangle. The bottom side goes from (4, 2) to (12, 2). The length is the difference in x-coordinates: 12 - 4 = 8 feet. Step 4: Find the width of the rectangle. The left side goes from (4, 2) to (4, 10). The width is the difference in y-coordinates: 10 - 2 = 8 feet. Step 5: Calculate the area. Area of a rectangle = length × width = 8 × 8 = 64. The area of the rectangular frame is 64 square feet.

6. Find the perimeter of a rectangle with vertices at (2, 3), (7, 3), (7, 8), and (2, 8) on the coordinate plane. Answer: 20 Solution: Identify the coordinates of the rectangle. The vertices are: A = (2, 3), B = (7, 3), C = (7, 8), D = (2, 8). Find the length of side AB.
   Full step-by-step solution

   Step 1: Identify the coordinates of the rectangle. The vertices are: A = (2, 3), B = (7, 3), C = (7, 8), D = (2, 8). Step 2: Find the length of side AB. Points A and B have the same y-coordinate (3), so the length is the difference in x-coordinates. Length AB = 7 - 2 = 5. Step 3: Find the length of side BC. Points B and C have the same x-coordinate (7), so the length is the difference in y-coordinates. Length BC = 8 - 3 = 5. Step 4: Check if the rectangle has sides of equal length for opposite sides. Since it is a rectangle, opposite sides are equal. So, length CD = length AB = 5, and length DA = length BC = 5. Step 5: Alternatively, verify with another side for clarity. Points C = (7, 8) and D = (2, 8) have the same y-coordinate (8), so length CD = 7 - 2 = 5. Points D = (2, 8) and A = (2, 3) have the same x-coordinate (2), so length DA = 8 - 3 = 5. Step 6: Calculate the perimeter. Perimeter of a rectangle = 2 * (length + width) = 2 * (5 + 5) = 2 * 10 = 20. Final Answer: 20

7. Plot the points (1, 6), (1, 16), (11, 16), and (11, 6) on a coordinate plane. What shape is formed and what is its area? Answer: square, 100 Solution: Plot the points (1,6), (1,16), (11,16), and (11,6). Connect them in order: (1,6) to (1,16) to (11,16) to (11,6) and back to (1,6). The shape has all right angles and opposite sides parallel.
   Full step-by-step solution

   Step 1: Plot the points (1,6), (1,16), (11,16), and (11,6). Connect them in order: (1,6) to (1,16) to (11,16) to (11,6) and back to (1,6). Step 2: The shape has all right angles and opposite sides parallel. Check side lengths: - Vertical side from (1,6) to (1,16): 16 - 6 = 10 units - Horizontal side from (1,16) to (11,16): 11 - 1 = 10 units - All sides are 10 units, so it is a square. Step 3: Area of a square = side × side = 10 × 10 = 100 square units. The answer is square, 100.

8. Ava is helping her teacher design a rectangular bulletin board for the school hallway. She plots the four corners on a coordinate grid where each unit represents 1 foot. The corners are at A(1, 1), B(11, 1), C(11, 6), and D(1, 6). What is the area of the bulletin board in square feet? Answer: 50 Solution: Find the length of the bulletin board. The bottom side goes from A(1, 1) to B(11, 1). Since the y-coordinates are the same, subtract the x-coordinates: 11 - 1 = 10 feet.
   Full step-by-step solution

   Step 1: Find the length of the bulletin board. The bottom side goes from A(1, 1) to B(11, 1). Since the y-coordinates are the same, subtract the x-coordinates: 11 - 1 = 10 feet. Step 2: Find the width of the bulletin board. The left side goes from A(1, 1) to D(1, 6). Since the x-coordinates are the same, subtract the y-coordinates: 6 - 1 = 5 feet. Step 3: Calculate the area: Area = length × width = 10 × 5 = 50. The area of the bulletin board is 50 square feet.