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Coordinate Graphing

Grade 5 · Geometry · Worksheet 2

  1. Mere plots a right triangle on a coordinate plane in the first quadrant. The vertices of the triangle are at (10, 15), (10, 21), and (16, 15). What is the area of the triangle in square units? Answer: ______________
  2. 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: ______________
  3. Emma is designing a new playground on a coordinate plane. She marks the four corners of a rectangular sandbox at points A(3, 2), B(9, 2), C(9, 6), and D(3, 6). If each unit on the grid represents 2 feet, what is the area of Emma's sandbox in square feet? Answer: ______________
  4. Plot the points (2, 3), (5, 3), (5, 7), and (2, 7) on a coordinate plane and find the area of the shape formed = ? Answer: ______________
  5. Tane is helping to design a new community garden on a coordinate grid. The garden committee decides to plant a rectangular herb bed. Tane marks three corners of the herb bed at points A(12, 10), B(21, 10), and C(12, 17). What are the coordinates of the fourth corner, D, needed to complete the rectangle? Answer: ______________
  6. Liam is designing a garden plot on a coordinate plane. He marks the corners of a rectangular vegetable bed at points A(2, 3), B(8, 3), C(8, 7), and D(2, 7). What is the area of Liam's vegetable bed in square units? Answer: ______________
  7. 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: ______________
  8. Plot the points (4, 1), (9, 1), (9, 7), and (4, 7) on a coordinate plane. What shape is formed and what is its perimeter? Answer: ______________
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Answer Key & Explanations

Coordinate Graphing · Grade 5 · Worksheet 2

  1. Mere plots a right triangle on a coordinate plane in the first quadrant. The vertices of the triangle are at (10, 15), (10, 21), and (16, 15). What is the area of the triangle in square units? Answer: 18 Solution: Identify the vertices: (10, 15), (10, 21), and (16, 15). Notice that (10, 15) and (10, 21) have the same x-coordinate, so the distance between them is vertical: 21 - 15 = 6 units. This is one leg of the triangle.
    Full step-by-step solution

    Step 1: Identify the vertices: (10, 15), (10, 21), and (16, 15). Step 2: Notice that (10, 15) and (10, 21) have the same x-coordinate, so the distance between them is vertical: 21 - 15 = 6 units. This is one leg of the triangle. Step 3: Notice that (10, 15) and (16, 15) have the same y-coordinate, so the distance between them is horizontal: 16 - 10 = 6 units. This is the other leg of the triangle. Step 4: For a right triangle, the legs are the base and height. Area = (1/2) × base × height. Step 5: Calculate area = (1/2) × 6 × 6 = (1/2) × 36 = 18. The area of the triangle is 18 square units.

  2. 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

  3. Emma is designing a new playground on a coordinate plane. She marks the four corners of a rectangular sandbox at points A(3, 2), B(9, 2), C(9, 6), and D(3, 6). If each unit on the grid represents 2 feet, what is the area of Emma's sandbox in square feet? Answer: 96 Solution: Find the length of the rectangle using points A(3,2) and B(9,2). Since they have the same y-coordinate, the length is the difference in x-coordinates: 9 - 3 = 6 units.
    Full step-by-step solution

    Step 1: Find the length of the rectangle using points A(3,2) and B(9,2). Since they have the same y-coordinate, the length is the difference in x-coordinates: 9 - 3 = 6 units. Step 2: Find the width of the rectangle using points A(3,2) and D(3,6). Since they have the same x-coordinate, the width is the difference in y-coordinates: 6 - 2 = 4 units. Step 3: Calculate the area in grid units: Area = length × width = 6 × 4 = 24 square units. Step 4: Convert to real measurements using the scale. Each unit represents 2 feet, so each square unit represents 2 × 2 = 4 square feet. Step 5: Calculate the actual area: 24 square units × 4 square feet per unit = 96 square feet. The area of Emma's sandbox is 96 square feet.

  4. Plot the points (2, 3), (5, 3), (5, 7), and (2, 7) on a coordinate plane and find the area of the shape formed = ? Answer: 12 Solution: A = (2, 3) B = (5, 3) C = (5, 7) D = (2, 7) From A to B: move right, y constant at 3 From B to C: move up, x constant at 5 From C to D: move left, y constant at 7 From D to A: move down, x constant at 2 Between A(2, 3) and B(5, 3): difference in x = 5 - 2 = 3 So length = 3 Between B(5, 3) and…
    Full step-by-step solution

    Let's go step-by-step. --- **Step 1: Plot the points and identify the shape** Points: A = (2, 3) B = (5, 3) C = (5, 7) D = (2, 7) Plotting them in order: From A to B: move right, y constant at 3 From B to C: move up, x constant at 5 From C to D: move left, y constant at 7 From D to A: move down, x constant at 2 This forms a rectangle because: - AB is horizontal - BC is vertical - CD is horizontal - DA is vertical --- **Step 2: Find the side lengths** Horizontal side length: Between A(2, 3) and B(5, 3): difference in x = 5 - 2 = 3 So length = 3 Vertical side length: Between B(5, 3) and C(5, 7): difference in y = 7 - 3 = 4 So height = 4 --- **Step 3: Calculate area of rectangle** Area = length × height Area = 3 × 4 = 12 --- **Step 4: Conclusion** The shape is a rectangle with sides 3 and 4, so the area is 12. --- **Final Answer:** 12

  5. Tane is helping to design a new community garden on a coordinate grid. The garden committee decides to plant a rectangular herb bed. Tane marks three corners of the herb bed at points A(12, 10), B(21, 10), and C(12, 17). What are the coordinates of the fourth corner, D, needed to complete the rectangle? Answer: (21, 17) Solution: A rectangle has opposite sides that are parallel and equal in length. The three given points are A(12, 10), B(21, 10), and C(12, 17). Points A and B share the same y-coordinate (10), so they form the bottom side.
    Full step-by-step solution

    Step 1: A rectangle has opposite sides that are parallel and equal in length. The three given points are A(12, 10), B(21, 10), and C(12, 17). Points A and B share the same y-coordinate (10), so they form the bottom side. Points A and C share the same x-coordinate (12), so they form the left side. Step 2: The missing corner D must be directly across from A, opposite both B and C. It should have the same x-coordinate as B (21) and the same y-coordinate as C (17). Step 3: Therefore, the coordinates of the fourth corner D are (21, 17). The answer is (21, 17).

  6. Liam is designing a garden plot on a coordinate plane. He marks the corners of a rectangular vegetable bed at points A(2, 3), B(8, 3), C(8, 7), and D(2, 7). What is the area of Liam's vegetable bed in square units? Answer: 24 Solution: Identify the coordinates of the rectangle's corners. A(2, 3), B(8, 3), C(8, 7), D(2, 7). Notice that AB is a horizontal side because A and B have the same y-coordinate (y = 3).
    Full step-by-step solution

    Let's find the area of the rectangular vegetable bed step by step. Step 1: Identify the coordinates of the rectangle's corners. A(2, 3), B(8, 3), C(8, 7), D(2, 7). Step 2: Notice that AB is a horizontal side because A and B have the same y-coordinate (y = 3). The length of AB = difference in x-coordinates = 8 - 2 = 6 units. Step 3: Notice that BC is a vertical side because B and C have the same x-coordinate (x = 8). The length of BC = difference in y-coordinates = 7 - 3 = 4 units. Step 4: Since it's a rectangle, area = length × width. Length = 6 units, width = 4 units. Area = 6 × 4 = 24 square units. Step 5: Verify with other sides: CD is horizontal: C(8, 7) to D(2, 7) → length = 8 - 2 = 6 units. DA is vertical: D(2, 7) to A(2, 3) → length = 7 - 3 = 4 units. Same result. Final answer: 24

  7. 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.

  8. Plot the points (4, 1), (9, 1), (9, 7), and (4, 7) on a coordinate plane. What shape is formed and what is its perimeter? Answer: rectangle, 22 Solution: Plot the points (4,1), (9,1), (9,7), and (4,7). Connect the points in order: (4,1) to (9,1) to (9,7) to (4,7) and back to (4,1). The shape has all right angles and opposite sides equal, so it is a rectangle.
    Full step-by-step solution

    Step 1: Plot the points (4,1), (9,1), (9,7), and (4,7). Step 2: Connect the points in order: (4,1) to (9,1) to (9,7) to (4,7) and back to (4,1). Step 3: The shape has all right angles and opposite sides equal, so it is a rectangle. Step 4: Find the length: The x-coordinates change from 4 to 9, so length = 9 - 4 = 5 units. Step 5: Find the width: The y-coordinates change from 1 to 7, so width = 7 - 1 = 6 units. Step 6: Calculate perimeter: P = 2 × (length + width) = 2 × (5 + 6) = 2 × 11 = 22 units. The shape is a rectangle with a perimeter of 22 units.