Parallel and Perpendicular Lines

New York State Common Core Math Geometry, Module 4, Lesson 9

Worksheets for Geometry, Module 4, Lesson 9

Student Outcomes

• Students find the perimeter of a triangle in the coordinate plane using the distance formula.
• Students state and apply the formula for area of a triangle with vertices (0,0),(x1, y1), and (x2 , y2).

Perimeter and Area of Triangles in the Cartesian Plane

Classwork

Opening Exercise

Find the area of the shaded region

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Example

Consider a triangular region in the plane with vertices 𝑂(0, 0), 𝐴(5, 2), and 𝐵(3, 4). What is the perimeter of the triangular region?
What is the area of the triangular region?
Find the general formula for the area of the triangle with vertices 𝑂(0, 0), 𝐴(𝑥1, 𝑦1), and 𝐵(𝑥2, 𝑦2), as shown. Does the formula work for this triangle?

Exercise

Find the area of the triangles with vertices listed, first by finding the area of the rectangle enclosing the triangle and subtracting the area of the surrounding triangles, then by using the formula 1/2(𝑥1𝑦2− 𝑥2𝑦1).
a. 𝑂(0, 0), 𝐴(5, 6), 𝐵(4, 1)
b. 𝑂(0, 0), 𝐴(3, 2), 𝐵 (−2, 6)
c. 𝑂(0, 0), 𝐴(5,−3), 𝐵(−2, 6)

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