Perimeter

Learning Objectives Calculate the distance between two points on a coordinate plane using the Distance Formula. Identify the vertices of a polygon and determine the segments that form its sides. Calculate the length of each side of a polygon using the coordinates of its vertices. Determine the perimeter of any polygon by summing the lengths of its sides. Classify a triangle (scalene, isosceles, equilateral) based on its side lengths calculated from coordinates. Solve multi-step problems involving the perimeter of polygons in the coordinate plane. How does a land surveyor determine the exact boundary length of a property without a giant measuring tape? 🗺️ They use coordinates and geometry to calculate the perimeter! This tutorial connects the concept of perimeter with the co...

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(3, -4) is located 3 units to the right of the y-axis and 4 units below the x-axis. VerticesThe corner points of a polygon. Each vertex is represented by an ordered pair (x, y) on the coordinate plane.A triangle with vertices at A(0,0), B(4,0), and C(2,3) has three corners at those specific coordinate points. Side LengthThe length of a line segment connecting two consecutive vertices of a polygon. In the coordinate plane, this is the distance between the two points.For a square with vertices at (0,0) and (5,0), the length of that side is 5 units. PerimeterThe total dis...

The Distance Formula d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} Use this formula to find the length of any segment (side of a polygon) between two points (x₁, y₁) and (x₂, y₂). This is the primary tool for finding side lengths that are not perfectly horizontal or vertical. Perimeter Formula P = s_1 + s_2 + s_3 + ... + s_n The perimeter (P) of any polygon is the sum of the lengths of all its sides (s₁, s₂, etc.). After using the Distance Formula to find each side length, add them all together. Horizontal and Vertical Distance Shortcuts Horizontal: d = |x_2 - x_1| | Vertical: d = |y_2 - y_1| If two points share the same y-coordinate, the line between them is horizontal. If they share the same x-coordinate, the line is vertical. Use these simpler formulas to find their...