Area and perimeter in the coordinate plane: Set 1

Learning Objectives Calculate the perimeter of a polygon given its vertices in the coordinate plane by applying the Distance Formula. Determine the area of triangles and rectangles with horizontal or vertical sides. Apply the 'boxing in' (enclosure) method to find the area of any polygon. Decompose a complex polygon into simpler shapes (rectangles and triangles) to find its total area. Use the Shoelace Formula as an efficient method for calculating the area of a simple polygon. Verify the properties of a polygon (e.g., right angles) using slope to simplify area calculations. Ever wondered how a GPS calculates the area of a park or a property lot just from a few coordinates? 🗺️ Let's learn the geometry behind it! This tutorial reviews how to use coordinate geo...

TermDefinitionExample Coordinate PlaneA two-dimensional plane formed by the intersection of a horizontal line called the x-axis and a vertical line called the y-axis. Points are located using ordered pairs (x, y).The point P(4, -2) is located 4 units to the right of the origin and 2 units down. VerticesThe corner points of a polygon. In the coordinate plane, each vertex is represented by an ordered pair.A triangle could have vertices at A(0, 0), B(5, 0), and C(2, 3). PerimeterThe total distance around the exterior of a polygon. It is calculated by summing the lengths of all its sides.For a triangle with side lengths 3, 4, and 5, the perimeter is 3 + 4 + 5 = 12 units. AreaThe measure of the two-dimensional space enclosed within a polygon, measured in square units.A rectangle with a length...

Distance Formula d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} Use this formula to calculate the length of a line segment (the distance) between any two points (x₁, y₁) and (x₂, y₂). This is essential for finding the side lengths of a polygon to calculate its perimeter. Slope Formula m = \frac{y_2 - y_1}{x_2 - x_1} Use this formula to find the slope of a line segment. Slopes can be used to determine if sides are parallel (equal slopes) or perpendicular (slopes are negative reciprocals, e.g., 2/3 and -3/2), which helps identify shapes like rectangles and right triangles. Shoelace Formula A = \frac{1}{2} |(x_1y_2 + x_2y_3 + ... + x_ny_1) - (y_1x_2 + y_2x_3 + ... + y_nx_1)| A powerful method to find the area of any simple polygon given its vertices (x₁, y₁), (x₂, y₂), ..., (...