If the coordinates of the vertices of a triangle are A(1, 1), B(4, 1), and C(1,

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Question: If the coordinates of the vertices of a triangle are A(1, 1), B(4, 1), and C(1, 5), what is the perimeter of the triangle?

Options:

Correct Answer: 12

Solution:

Length AB = 3, Length AC = 4, Length BC = √((4-1)² + (1-5)²) = √(9 + 16) = 5. Perimeter = 3 + 4 + 5 = 12.

If the coordinates of the vertices of a triangle are A(1, 1), B(4, 1), and C(1, 5), what is the perimeter of the triangle?

If the coordinates of the vertices of a triangle are A(1, 1), B(4, 1), and C(1, 5), what is the perimeter of the triangle?

Step 1: Identify the coordinates of the triangle's vertices. A is at (1, 1), B is at (4, 1), and C is at (1, 5).
Step 2: Calculate the length of side AB. Use the formula: Length = x2 - x1. Here, x1 = 1 and x2 = 4. So, Length AB = 4 - 1 = 3.
Step 3: Calculate the length of side AC. Use the formula: Length = y2 - y1. Here, y1 = 1 and y2 = 5. So, Length AC = 5 - 1 = 4.
Step 4: Calculate the length of side BC using the distance formula: Length BC = √((x2 - x1)² + (y2 - y1)²). Here, B is (4, 1) and C is (1, 5). So, Length BC = √((4 - 1)² + (1 - 5)²) = √(3² + (-4)²) = √(9 + 16) = √25 = 5.
Step 5: Add the lengths of all sides to find the perimeter. Perimeter = Length AB + Length AC + Length BC = 3 + 4 + 5 = 12.

Distance Formula – The distance between two points in a Cartesian plane 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 sides.
Coordinate Geometry – Understanding how to plot points and calculate distances in a coordinate system.