If a triangle has vertices at (1, 2), (4, 6), and (7, 2), what is its perimeter?

If a triangle has vertices at (1, 2), (4, 6), and (7, 2), what is its perimeter?

Step 1: Identify the vertices of the triangle. They are A(1, 2), B(4, 6), and C(7, 2).
Step 2: Use the distance formula to find the length of side AB. The formula is AB = √((x2 - x1)² + (y2 - y1)²). Here, (x1, y1) = (1, 2) and (x2, y2) = (4, 6).
Step 3: Calculate AB: AB = √((4 - 1)² + (6 - 2)²) = √(3² + 4²) = √(9 + 16) = √25 = 5.
Step 4: Use the distance formula to find the length of side BC. Here, (x1, y1) = (4, 6) and (x2, y2) = (7, 2).
Step 5: Calculate BC: BC = √((7 - 4)² + (2 - 6)²) = √(3² + (-4)²) = √(9 + 16) = √25 = 5.
Step 6: Use the distance formula to find the length of side CA. Here, (x1, y1) = (7, 2) and (x2, y2) = (1, 2).
Step 7: Calculate CA: CA = √((1 - 7)² + (2 - 2)²) = √((-6)² + 0²) = √(36 + 0) = √36 = 6.
Step 8: Add the lengths of all sides to find the perimeter: Perimeter = AB + BC + CA = 5 + 5 + 6 = 16.

Distance Formula – The distance between two points (x1, y1) and (x2, y2) is calculated using the formula √((x2 - x1)² + (y2 - y1)²).
Perimeter of a Triangle – The perimeter of a triangle is the sum of the lengths of its three sides.