Question: If a triangle has vertices at (1, 1), (4, 1), and (1, 5), what is its perimeter?
Options:
12
10
14
8
Correct Answer: 10
Solution:
Perimeter = AB + BC + CA = 3 + 3 + 4 = 10.
If a triangle has vertices at (1, 1), (4, 1), and (1, 5), what is its perimeter?
Practice Questions
Q1
If a triangle has vertices at (1, 1), (4, 1), and (1, 5), what is its perimeter?
12
10
14
8
Questions & Step-by-Step Solutions
If a triangle has vertices at (1, 1), (4, 1), and (1, 5), what is its perimeter?
Step 1: Identify the vertices of the triangle. The vertices are A(1, 1), B(4, 1), and C(1, 5).
Step 2: Calculate the distance between points A and B (AB). Use the distance formula: AB = √((x2 - x1)² + (y2 - y1)²). Here, A(1, 1) and B(4, 1). So, AB = √((4 - 1)² + (1 - 1)²) = √(3² + 0²) = √9 = 3.
Step 3: Calculate the distance between points B and C (BC). Use the distance formula: BC = √((x2 - x1)² + (y2 - y1)²). Here, B(4, 1) and C(1, 5). So, BC = √((1 - 4)² + (5 - 1)²) = √((-3)² + 4²) = √(9 + 16) = √25 = 5.
Step 4: Calculate the distance between points C and A (CA). Use the distance formula: CA = √((x2 - x1)² + (y2 - y1)²). Here, C(1, 5) and A(1, 1). So, CA = √((1 - 1)² + (1 - 5)²) = √(0² + (-4)²) = √16 = 4.
Step 5: Add the lengths of all sides to find the perimeter. Perimeter = AB + BC + CA = 3 + 5 + 4 = 12.
Distance Formula – The perimeter of a triangle is calculated by finding the lengths of its sides using the distance formula between points in a Cartesian plane.
Triangle Properties – Understanding the properties of triangles, including how to calculate the perimeter by summing the lengths of all sides.
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