 # Drawing Polygons in the Coordinate Plane

Videos and solutions to help Grade 6 students draw polygons in the coordinate plane and find the area enclosed by a polygon by composing or decomposing using polygons with known area formulas.

New York State Common Core Math Module 5, Grade 6, Lesson 8

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Common Core For Grade 6

Lesson 8 Student Outcomes

• Given coordinates for the vertices, students draw polygons in the coordinate plane. Students find the area enclosed by a polygon by composing or decomposing using polygons with known area formulas.
• Students name coordinates that define a polygon with specific properties.

Lesson 8 Classwork
Examples:

1. Plot and connect the points A(3, 2), B(3, 7), and C(8, 2). Name the shape and determine the area of the polygon.

2. Plot and connect the points E(-8, 8), F(-2, 5), and G(-7, 2). Then give the best name for the polygon and determine the area.

3. Plot the following points: K(-10, -9), L(-8, -2), M(-3, -6), and N(-7, -6). Give the best name for the polygon and determine the area.

4. Plot the following points: P(1, -4), Q(5, -2), R(9, -4), S(7, -8), and T(3, -8). Give the best name for the polygon and determine the area.

5. Two of the coordinates of a rectangle are A(3, 7) and B(3, 2). The rectangle has an area of 30 square units. Give the possible locations of the other two vertices by identifying their coordinates. (Use the coordinate plane to draw out and check your answer.)

Exercises

For Problems 1 and 2, plot the points, name the shape, and determine the area of the shape. Then write an expression that could be used to determine the area of the figure. Explain how each part of the expression corresponds to the situation.

3. A rectangle with vertices located at (-3, 4) and (5, 4) has an area of 32 square units. Determine the location of the other two vertices.

4. Challenge: A triangle with vertices located at (-2, -3) and (3, -3) has an area of square units. Determine one possible location of the other vertex.

Problem Set
Plot the points for each shape, determine the area of the polygon, and then write an expression that could be used to determine the area of the figure. Explain how each part of the expression corresponds to the situation.

1. A(1,3), B(2,8), C(8,8), D(10,3), and E(5,-2)

2. X(-10,2), Y(-3,6), and Z(-6,-5)

3. (5,7), F(9,-5), and G(1,-3)

4. Find the area of the triangle in Problem 3 using a different method. Then, compare the expressions that can be used for both solutions in Problems 3 and 4

5. Two vertices of a rectangle are (8,-5) and (8,7). If the area of the rectangle is 72 square units, name the possible location of the other two vertices.

6. A triangle with two vertices located at (5,-8) and (5,4) has an area of 48 square units. Determine one possible location of the other vertex.

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